General
✓✗Two cars P and Q start from a point at the same time in a straight line and their positions are represented by \( x_P(t) = at + bt^2 \) and \( x_Q(t) = ft - t^2 \). At what time do the cars have the same velocity?
- \( \dfrac{a + f}{2(1 + b)} \)
- \( \dfrac{a + f}{2(b - 1)} \)
- \( \dfrac{a - f}{1 + b} \)
- \( \dfrac{f - a}{2(1 + b)} \)
General
✓✗A particle moves along a straight line OX. At a time t (in seconds), the distance x (in metres) of the particle from O is given by \( x = 40 + 12t - t^3 \). How far would the particle travel before coming to rest?
- 16 m
- 40 m
- 24 m
- 56 m
General
✓✗For a body moving with uniform acceleration, the velocity-time graph is
- a hyperbola
- a straight line inclined to the time axis
- a parabola
- parallel to the time axis
General
✓✗The slope of a position-time graph at an instant gives the
- displacement
- acceleration
- distance
- instantaneous velocity
General
✓✗The velocity of a particle is given by \( v = 3t^2 + 2t \) m/s. Its displacement from t = 0 to t = 2 s is
- 16 m
- 12 m
- 8 m
- 10 m
General
✓✗A cyclist rides 4 km at 8 km/h and then 4 km at 16 km/h. His average speed is
- 10 km/h
- \( \dfrac{16}{3} \) km/h
- \( \dfrac{32}{3} \) km/h
- 12 km/h
General
✓✗The velocity of a particle is \( v = 3t^2 - 6t \) m/s. Its acceleration when its velocity is zero (t > 0) is
- 6 m s−2
- 0
- −6 m s−2
- 12 m s−2
General
✓✗The kinematic equation \( v^2 = u^2 + 2as \) does NOT contain
- displacement
- initial velocity
- acceleration
- time
General
✓✗Assertion: For a body thrown vertically upwards, the time of ascent equals the time of descent (no air resistance).
Reason: The acceleration is the same (g downward) during ascent and descent.
Reason: The acceleration is the same (g downward) during ascent and descent.
- Both Assertion and Reason are true and Reason is the correct explanation of Assertion
- Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
- Assertion is true but Reason is false
- Both Assertion and Reason are false
General
✓✗Two trains move towards each other on parallel tracks with speeds of 50 km/h and 70 km/h. The speed of one with respect to the other is
- 20 km/h
- 120 km/h
- 35 km/h
- 60 km/h
General
✓✗A person walks 3 km due north and then 4 km due south. His displacement is
- 7 km south
- 7 km north
- 1 km south
- 1 km north
General
✓✗A particle moves with a retardation proportional to its velocity, \( a = -kv \). Its velocity as a function of time, starting with v0, is
- \( v_0e^{kt} \)
- \( v_0 - kt \)
- \( \dfrac{v_0}{1 + kt} \)
- \( v_0e^{-kt} \)
General
✓✗Assertion: A body moving with uniform speed along a circular track has zero average velocity over one complete revolution.
Reason: The displacement in one complete revolution is zero.
Reason: The displacement in one complete revolution is zero.
- Both Assertion and Reason are true and Reason is the correct explanation of Assertion
- Both Assertion and Reason are true but Reason is not the correct explanation of Assertion
- Assertion is true but Reason is false
- Both Assertion and Reason are false
General
✓✗A stone is dropped from a tower of height 80 m. One second later another stone is thrown vertically down from the same point. With what speed must it be thrown so that both stones reach the ground together? (take g = 10 m s−2)
- \( \dfrac{40}{3} \) m/s
- 10 m/s
- 15 m/s
- \( \dfrac{35}{3} \) m/s
General
✓✗A particle has velocity \( v = 4 - 2t \) m/s. The distance it covers between t = 0 and t = 3 s is
- 6 m
- 4 m
- 3 m
- 5 m