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Mock Test — Advanced Motion Concepts

Section A: Foundations

Question 1mcq
With downward chosen positive, what is the acceleration of a freely falling body?
A.+g+g
B.−g-g
C.00
D.−2g-2g
Question 2mcq
If a position-time graph is horizontal, its derivative is?
A.11
B.00
C.Constant but non-zero
D.Undefined
Question 3mcq
A horizontal velocity-time graph above the time axis represents?
A.Constant positive acceleration
B.Object at rest
C.Constant positive velocity
D.Negative velocity
Question 4mcq
A ball thrown upward with u=20 m/su=20\,m/s has maximum height, for g=10 m/s2g=10\,m/s^2, equal to?
A.10 m10\,m
B.40 m40\,m
C.200 m200\,m
D.20 m20\,m
Question 5mcq
For x=7t−2x=7t-2, velocity is?
A.77
B.7t7t
C.−2-2
D.55
Question 6mcq
The slope of a position-time graph is negative. The object is moving?
A.With positive acceleration only
B.In the negative direction
C.At rest
D.With zero speed
Question 7mcq
A stone falls freely for 2 s2\,s. Its speed for g=10 m/s2g=10\,m/s^2 is?
A.5 m/s5\,m/s
B.10 m/s10\,m/s
C.20 m/s20\,m/s
D.40 m/s40\,m/s
Question 8mcq
If v=9−2tv=9-2t, acceleration is?
A.2 m/s22\,m/s^2
B.9 m/s29\,m/s^2
C.00
D.−2 m/s2-2\,m/s^2
Question 9mcq
Area under a velocity-time graph has SI unit?
A.mm
B.m/sm/s
C.m/s2m/s^2
D.ss
Question 10mcq
Which rule is suitable for differentiating x=t(t2+1)x=t(t^2+1)?
A.Only constant rule
B.Product rule
C.No rule is needed because derivative is zero
D.Integration rule

Section B: Core Applications

Question 11mcq
How far does a freely falling body travel in its second second? Take g=10 m/s2g=10\,m/s^2.
A.5 m5\,m
B.10 m10\,m
C.15 m15\,m
D.20 m20\,m
Question 12mcq
For x=2t2−3t+1x=2t^2-3t+1, velocity at t=2 st=2\,s is?
A.1 m/s1\,m/s
B.4 m/s4\,m/s
C.8 m/s8\,m/s
D.5 m/s5\,m/s
Question 13mcq
A velocity-time graph forms a rectangle of height 6 m/s6\,m/s and width 5 s5\,s. Its area is?
A.30 m30\,m
B.11 m11\,m
C.1.2 m1.2\,m
D.36 m36\,m
Question 14mcq
Two stones are dropped from the same point 2 s2\,s apart. Four seconds after the first release, their separation is? Take g=10 m/s2g=10\,m/s^2.
A.20 m20\,m
B.60 m60\,m
C.40 m40\,m
D.80 m80\,m
Question 15mcq
If x=(t+2)3x=(t+2)^3, velocity is?
A.(t+2)2(t+2)^2
B.3t2+23t^2+2
C.3(t+2)23(t+2)^2
D.3(t+2)3(t+2)
Question 16mcq
Velocity changes from 12 m/s12\,m/s to 4 m/s4\,m/s in 2 s2\,s. Graph slope is?
A.4 m/s24\,m/s^2
B.−8 m/s2-8\,m/s^2
C.8 m/s28\,m/s^2
D.−4 m/s2-4\,m/s^2
Question 17mcq
A ball returns to its launch point after 8 s8\,s. For g=10 m/s2g=10\,m/s^2, its initial speed was?
A.40 m/s40\,m/s
B.20 m/s20\,m/s
C.60 m/s60\,m/s
D.80 m/s80\,m/s
Question 18mcq
If v=4tv=4t, displacement from 00 to 3 s3\,s is?
A.12 m12\,m
B.18 m18\,m
C.24 m24\,m
D.36 m36\,m
Question 19mcq
A velocity-time graph crosses from positive to negative values. What definitely occurs?
A.The object’s mass changes.
B.Acceleration becomes zero forever.
C.The object reverses direction.
D.Distance becomes negative.
Question 20mcq
A ball is thrown downward at 10 m/s10\,m/s from a height and falls for 3 s3\,s. Take g=10 m/s2g=10\,m/s^2. Distance covered is?
A.45 m45\,m
B.60 m60\,m
C.90 m90\,m
D.75 m75\,m
Question 21mcq
For x=(t+1)(2t−3)x=(t+1)(2t-3), velocity is?
A.4t−14t-1
B.2t−22t-2
C.4t+14t+1
D.2t2−t−32t^2-t-3
Question 22mcq
An acceleration of 3 m/s23\,m/s^2 acts for 4 s4\,s. The area under the a−ta-t graph gives a velocity change of?
A.7 m/s7\,m/s
B.12 m/s12\,m/s
C.3/4 m/s3/4\,m/s
D.1 m/s1\,m/s
Question 23mcq
A ball moving downward has velocity −12 m/s-12\,m/s when upward is positive. One second later, with g=10 m/s2g=10\,m/s^2, velocity is?
A.−2 m/s-2\,m/s
B.2 m/s2\,m/s
C.−22 m/s-22\,m/s
D.22 m/s22\,m/s
Question 24mcq
A velocity-time graph has equal triangular areas above and below the time axis. Net displacement is?
A.Equal to total distance
B.Always positive
C.Undefined
D.00
Question 25mcq
A straight velocity-time graph has intercept 55 and slope 22. Which equation matches it?
A.v=5+2tv=5+2t
B.v=2+5tv=2+5t
C.v=5−2tv=5-2t
D.v=10tv=10t

Section C: Advanced Reasoning

Question 26mcq
A ball passes the same height at t=2 st=2\,s and t=8 st=8\,s. For g=10 m/s2g=10\,m/s^2, its initial speed is?
A.30 m/s30\,m/s
B.50 m/s50\,m/s
C.40 m/s40\,m/s
D.100 m/s100\,m/s
Question 27mcq
For x=t3−6t2+9tx=t^3-6t^2+9t, acceleration at the first instant of rest is?
A.00
B.6 m/s26\,m/s^2
C.−6 m/s2-6\,m/s^2
D.12 m/s212\,m/s^2
Question 28mcq
A velocity-time graph has positive area 30 m30\,m and negative area 12 m12\,m. What are displacement and total distance?
A.42 m42\,m and 18 m18\,m
B.18 m18\,m and 18 m18\,m
C.30 m30\,m and 12 m12\,m
D.18 m18\,m and 42 m42\,m
Question 29mcq
A body covers 55 m55\,m in its sixth second of free fall. What is gg?
A.10 m/s210\,m/s^2
B.5 m/s25\,m/s^2
C.11 m/s211\,m/s^2
D.20 m/s220\,m/s^2
Question 30mcq
For x=(t2+2t)2x=(t^2+2t)^2, velocity at t=1 st=1\,s is?
A.12 m/s12\,m/s
B.24 m/s24\,m/s
C.18 m/s18\,m/s
D.36 m/s36\,m/s
Question 31mcq
An acceleration-time graph has area +8 m/s+8\,m/s from 00–4 s4\,s and area −3 m/s-3\,m/s from 44–6 s6\,s. If initial velocity is 2 m/s2\,m/s, final velocity is?
A.3 m/s3\,m/s
B.5 m/s5\,m/s
C.7 m/s7\,m/s
D.13 m/s13\,m/s
Question 32mcq
A stone is dropped from 80 m80\,m. Simultaneously another is thrown upward from ground at 30 m/s30\,m/s. When do they meet?
A.2 s2\,s
B.3 s3\,s
C.4 s4\,s
D.83 s\frac{8}{3}\,s

Section D: Challenge Set

Question 33mcq
For v=t2−4t+3v=t^2-4t+3, what is displacement from t=0t=0 to t=3 st=3\,s?
A.00
B.3 m3\,m
C.6 m6\,m
D.9 m9\,m
Question 34mcq
A position-time graph has a smooth maximum. What is true at the maximum?
A.Acceleration must be zero.
B.Velocity is zero and changes sign.
C.Displacement is zero.
D.Speed is maximum.
Question 35mcq
A stone released from a rising balloon at 20 m/s20\,m/s takes 6 s6\,s to hit ground. What was the release height? Take g=10 m/s2g=10\,m/s^2.
A.40 m40\,m
B.120 m120\,m
C.60 m60\,m
D.180 m180\,m
Question 36mcq
For x=t2(t−3)x=t^2(t-3), at what non-zero time is velocity zero?
A.1 s1\,s
B.3 s3\,s
C.6 s6\,s
D.2 s2\,s
Question 37mcq
A v−tv-t graph rises linearly from −4-4 to 8 m/s8\,m/s over 6 s6\,s. What is the net displacement?
A.12 m12\,m
B.6 m6\,m
C.18 m18\,m
D.24 m24\,m
Question 38mcq
A ball thrown upward reaches maximum height 45 m45\,m. For g=10 m/s2g=10\,m/s^2, its initial speed is?
A.15 m/s15\,m/s
B.30 m/s30\,m/s
C.45 m/s45\,m/s
D.90 m/s90\,m/s
Question 39mcq
Velocity is v=∣t−3∣v=|t-3| from t=0t=0 to t=6t=6. What is displacement?
A.00
B.6 m6\,m
C.9 m9\,m
D.18 m18\,m
Question 40mcq
A position-time graph follows x=2t2x=2t^2. What is the velocity-time graph?
A.A horizontal line at 22.
B.A parabola opening upward.
C.A straight line with slope 22 and intercept 22.
D.A straight line through the origin with slope 44.