NCERT Solutions

My father went to a shop from home which is located at a distance of 250 m on a straight road. On reaching there, he discovered that he forgot to carry a cloth bag. He came home to take it, went to the shop again, bought provisions and came back home. How much was the total distance travelled by him? What was his displacement from home?

A girl is riding her scooter and finds that its speedometer reading is constant. Is it possible for her scooter to be accelerating and if so, how?

A car starts from rest and its velocity reaches $24 \text{ m s}^{-1}$ in 6 s. Find the average acceleration and the distance travelled in these 6 s.

A motorbike moving with initial velocity $28 \text{ m s}^{-1}$ and constant acceleration stops after travelling 98 m. Find the acceleration of the motorbike and the time taken to come to a stop.

Fig. 4.27 shows a position-time graph of two objects A and B that are moving along the parallel tracks in the same direction. Do objects A and B ever have equal velocity? Justify your answer.

A truck driver driving at the speed of $54 \text{ km h}^{-1}$ notices a road sign with a speed limit of $40 \text{ km h}^{-1}$ (Fig. 4.29) for trucks. He slows down to $36 \text{ km h}^{-1}$ in 36 s. What was the distance travelled by him during this time? Assume the acceleration to be constant while slowing down.

A car starts from rest and accelerates uniformly to $20 \text{ m s}^{-1}$ in 5 seconds. It then travels at $20 \text{ m s}^{-1}$ for 10 seconds and finally applies the brake (with uniform acceleration) to stop in 6 seconds. Find the total distance travelled.

A bus is travelling at $36 \text{ km h}^{-1}$ when the driver sees an obstacle 30 m ahead. The driver takes 0.5 seconds to react before pressing the brake. Once the brake is applied, the velocity of the bus reduces with constant acceleration of $2.5 \text{ m s}^{-2}$. Will the bus be able to stop before reaching the obstacle?

A student said, "The Earth moves around the Sun". In this context, discuss whether an object kept on the Earth can be considered to be at rest.

A girl is preparing for her first marathon by running on a straight road. She uses a smartwatch to calculate her running speed at different intervals. The graph (Fig. 4.31) depicts her velocity versus time. Estimate the distance she ran based on the graph.

On entering a state highway, a car continues to move with a constant velocity of $6 \text{ m s}^{-1}$ for 2 minutes and then accelerates with a constant acceleration $1 \text{ m s}^{-2}$ for 6 seconds. Find the displacement of the car on the state highway in the 2 min 6 s time interval by drawing a velocity-time graph for its motion.

Two cars A and B start moving with a constant acceleration from rest, in a straight line. Car A attains a velocity of $5 \text{ m s}^{-1}$ in 5 s. Car B attains a velocity of $3 \text{ m s}^{-1}$ in 10 s. Plot the velocity-time graphs for both the cars in the same graph. Using the graph, calculate the displacement in the two time intervals mentioned (Hint: Calculate the acceleration in both cases. Then calculate their velocities at five instants of time to plot the graph).