General
✓✗The position of a particle is \( x = 2t^3 - 9t^2 + 12t \) m. Between t = 0 and t = 3 s, the particle changes its direction of motion
- once
- three times
- never
- twice
General
✓✗A particle is at x = 5 m at t = 0, at x = −7 m at t = 6 s and at x = 2 m at t = 10 s. Its average velocity between t = 0 and t = 10 s is
- −1.2 m/s
- −0.3 m/s
- 2.1 m/s
- 0.3 m/s
General
✓✗A body is dropped from a height h. In the last second it covers 9h/25. The value of h is (take g = 10 m s−2)
- 45 m
- 80 m
- 125 m
- 100 m
General
✓✗The area under an acceleration-time graph gives the
- jerk
- displacement
- change in velocity
- distance
General
✓✗If a ball is thrown vertically upwards with speed u, the distance covered during the last t seconds of its ascent is
- \( ut \)
- \( \dfrac{1}{2}gt^2 \)
- \( ut - \dfrac{1}{2}gt^2 \)
- \( (u + gt)t \)
General
✓✗The position-time graph of a particle is a straight line parallel to the position axis. This represents
- a body at rest
- infinite acceleration only
- uniform velocity
- an impossible motion
General
✓✗The acceleration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an initial velocity v0. The distance travelled by the particle in time t will be
- \( v_0t + \dfrac{1}{3}bt^2 \)
- \( v_0t + \dfrac{1}{6}bt^3 \)
- \( v_0t + \dfrac{1}{2}bt^2 \)
- \( v_0t + \dfrac{1}{3}bt^3 \)
General
✓✗A particle moves along a straight line. Which of the following statements are correct?
A. If its x-t graph is a straight line, its acceleration is zero.
B. If its v-t graph is a straight line, its acceleration is constant.
C. If its a-t graph is a straight line through the origin, its v-t graph is a parabola (starting from rest).
D. If its v-t graph is a parabola, its acceleration is constant.
Choose the correct answer from the options given below.
A. If its x-t graph is a straight line, its acceleration is zero.
B. If its v-t graph is a straight line, its acceleration is constant.
C. If its a-t graph is a straight line through the origin, its v-t graph is a parabola (starting from rest).
D. If its v-t graph is a parabola, its acceleration is constant.
Choose the correct answer from the options given below.
- A, B and C only
- A and D only
- B, C and D only
- A, B, C and D
General
✓✗The acceleration of a particle is \( a = 6t \) m s−2. If it starts from rest at the origin, its displacement after 2 s is
- 4 m
- 24 m
- 8 m
- 12 m
General
✓✗A ball thrown vertically upwards with speed 30 m/s returns to the thrower after (g = 10 m s−2)
- 6 s
- 9 s
- 4.5 s
- 3 s
General
✓✗A particle moves along x such that \( x = \alpha t^3 \). The ratio of its average velocity over the first t seconds to its instantaneous velocity at time t is
- 1 : 1
- 3 : 1
- 1 : 3
- 1 : 2
General
✓✗A body starting from rest covers distances in the ratio s1 : s2 : s3 in the first 1 s, first 2 s and first 3 s. This ratio is
- 1 : 3 : 5
- 1 : 8 : 27
- 1 : 2 : 3
- 1 : 4 : 9
General
✓✗For the motion \( x = \dfrac{1}{3}t^3 - 2t^2 + 3t \) m, the acceleration at the instant(s) when the particle is at rest is
- +2 m s−2 at both instants
- zero at both instants
- −2 m s−2 at t = 1 s and +2 m s−2 at t = 3 s
- −2 m s−2 at both instants
General
✓✗Statement I: A body thrown vertically upwards with speed u from the ground spends equal times above and below the height H/2, where H is its maximum height.
Statement II: The body spends more time in the upper half of its path than in the lower half.
Choose the correct answer.
Statement II: The body spends more time in the upper half of its path than in the lower half.
Choose the correct answer.
- Both Statement I and Statement II are correct
- Both Statement I and Statement II are incorrect
- Statement I is correct but Statement II is incorrect
- Statement I is incorrect but Statement II is correct
General
✓✗A particle moving with uniform acceleration covers 24 m in the first 4 s and 64 m in the next 4 s. Its acceleration is
- 2 m s−2
- 5 m s−2
- 1.5 m s−2
- 2.5 m s−2