Q. The following is the distance-times table of an object in motion:
Time in seconds Distance in metres
$0$ $0$
$1$ $1$
$2$ $8$
$3$ $27$
$4$ $64$
$5$ $125$
$6$ $216$
$7$ $343$
$\left(a\right)$ What conclusion can you draw about the acceleration? Is it constant, increasing, decreasing, or zero?
$\left(b\right)$ What do you infer about the forces acting on the object?

Q. A $8000$kg engine pulls a train of $5$ wagons, each of $2000$kg, along a horizontal track. If the engine exerts a force of $40000$N and the track offers a friction force of $5000$N, then calculate:
$\left(a\right)$ The net accelerating force:
$\left(b\right)$ The acceleration of the train; and
$\left(c\right)$ The force of wagon $1$ on wagon $2$.

Q. An automobile vehicle has a mass of $1500$kg. What must be the force between the vehicle and road if the vehicle is to be stopped with a negative acceleration of $1.7{ms}^{-2}$?

Q. An object of mass $1$kg travelling in a straight line with a velocity of $10$m $s^{-1}$ collides with and sticks to a stationary wooden block of mass $5$kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.

Q. A hammer of mass $500g,$ moving at $50{ms}^{-1},$ strikes a nail. The nail stops the hammer in a very short time of $0.01s.$ What is the force of the nail on the hammer?

Q. How much momentum will a dumb-bell of mass $10$kg transfer to the floor if it falls from a height of $80$cm ? Take its downward acceleration to be $10$m $s^{-2}$

Q. A motorcar of mass $1200$kg is moving along a straight line with a uniform velocity of $90$km/h. Its velocity is slowed down to $18$km/h in $4$s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required.

Q. An object of mass $100kg$ is accelerated uniformly from a velocity of $5{ms}^{-1}$ to $8{ms}^{-1}$ in $6s$. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.

Q. According to the third law of motion when we push on an object, the object pushes back on us with an equal and opposite force. If the object is a massive truck parked along the roadside, it will probably not move. A student justifies this by answering that the two opposite and equal forces cancel each other. Comment on this logic and explain why the truck does not move.

Q. An object experience a net zero external unbalanced force. Is it possible for the object to be travelling with a non-zero velocity? If yes, state the conditions that must be placed on the magnitude and direction of the velocity. If no, provide a reason.

Q. A stone of $1$kg is thrown with a velocity of $20$m $s^{-1}$ across the frozen surface of a lake and comes to rest after travelling a distance of $50$m. What is the force of friction between the stone and the ice?

Q. A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of $400$m in $20$s. Find the acceleration. Find the force acting on it if its mass is $7$ tonnes. (Hint: 1 tonne = 1000 kg.)

Q. Using a horizontal force of $200$N, we intend to move a wooden cabinet across a floor at a constant velocity. What is the friction force that will be exerted on the cabinet?

Q. When a carpet is beaten with a stick, dust comes out of it. Explain.

Q. Why is it advised to tie any luggage kept on the roof of a bus with a rope?

Q. Two persons manage to push a motorcar of mass $1200$kg at a uniform velocity along a level road. The same motorcar can be pushed by three persons to produce an acceleration of $0.2$m $s^{-2}$. With what force does each person push the motorcar? (Assume that all persons push the motorcar with the same muscular effort.)

Q. Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar(because the change in the velocity of the insect was much more than that of the motorcar). Akhtar said that since the motorcar was moving with a larger velocity, it exerted a larger force on the insect. And as a result the insect died. Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions.

Q. Two objects, each of mass $1.5$kg, are moving in the same straight line but in opposite directions. The velocity of each object is $2.5$m $s^{-1}$ before the collision during which they stick together. What will be the velocity of the combined object after collision?

Q. A hockey ball of mass $200$g travelling at $10$m $s^{-1}$ is struck by a hockey stick so as to return it along its original path with a velocity at $5$m $s^{-1}$. Calculate the change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick.

Q. A bullet of mass $10g$ travelling horizontally with a velocity of $150{ms}^{-1}$ strikes a stationary wooden block and comes to rest in $0.03s$. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet.