The relation between time t and distance x is t=ax^{2} +bx where a and b are constants. The acceleration is
−2abv^{2}
2bv^{3}
−2av^{3}
2av^{2}
C.
−2av^{3}
A projectile can have the same range R for two angles of projection. If T_{1} and T_{2} be the time of flights in the two cases, then the product of the two time of flights is directly proportional to
1/R^{2}
1/R
R
R^{2}
C.
R
We know in advance that range of projectile is same for complementary angles i.e. for θ and (900 - θ )
Which of the following statements is false for a particle moving in a circle with a constant angular speed?
The velocity vector is tangent to the circle.
The acceleration vector is tangent to the circle.
The acceleration vector points to the centre of the circle.
The velocity and acceleration vectors are perpendicular to each other.
B.
The acceleration vector is tangent to the circle.
A projectile can have the same range R for two angles of projection. If t_{1} and t_{2} be the times of flights in the two cases, then the product of the two time of flights is proportional to
R^{2}
1/R^{2}
1/R
R
D.
R
A parachutist after bailing outfalls 50 m without friction. When a parachute opens, it decelerates at 2 m/s^{2}. He reaches the ground with a speed of 3 m/s. At what height, did he bail out?
91 m
182 m
293 m
111 m
C.
293 m
A particle is moving eastwards with a velocity of 5 m/s in 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is
zero
D.
towards north-westA car starting from rest accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance traversed is 15 S, then
S=ft
S= ft^{2}/72
S = 1/2 ft^{2}
S = 1/4 ft^{2}
B.
S= ft^{2}/72
A body of mass m accelerates uniformly from rest to v_{1} in time t_{1}. The instantaneous power delivered to the body as a function of time t is
B.
Let the constant acceleration of body of mass m is a.
From equation of motion
v_{1} = 0 + at_{1}
⇒ a = t_{2}/t_{1 }= ...... (i)
At an instant t, the velocity v of the body v = 0 + at
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particle takes place in a plane. It follows that
its velocity is constant
its acceleration is constant
its kinetic energy is constant
it moves in a straight line.
C.
its kinetic energy is constant
When a force of constant magnitude acts on the velocity of particle perpendicularly, then there is no change in the kinetic energy of the particle. Hence, kinetic energy remains constant.