Non Uniform Motion & Avg Velocity

Q. Between the two stations, a train accelerates from rest uniformly at first, then moves with constant velocity and finally retards uniformly to come to rest. If the ratio of the time taken be $1:8:1$ and the maximum speed attained be $60\text{km/h}$, then, what is the average speed over the whole journey?

1. $48\text{km/hr}$
2. $52\text{km/hr}$
3. $54\text{km/hr}$
4. $56\text{km/hr}$

Q. A particle moving in a straight line covers half the distance with speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is

1. 4.0 m/s
2. 5.0 m/s
3. 5.5 m/s
4. 4.8 m/s

Q.

A boy walks to his school at a distance of 6 km with constant speed of 2.5 km/hour and walks back with a constant speed of 4 km/hr. His average speed for round trip expressed in km/hr, is

1. $\frac{24}{13}$

2. $\frac{40}{13}$

3. 3

4. $\frac{1}{2}$

Q.

A person travels along a straight road for half the distance with velocity $v_1$ and the remaining half distance with velocity $v_2$ The average velocity is given by

1. $v_1{v}_2$

2. $\frac{v_2{}^2}{v_1{}^2}$

3. $\frac{v_1+v_2}{2}$

4. $\frac{2v_1{v}_2}{v_1+v_2}$

Q.

A particle is constrained to move on a straight line path. It returns to the starting point after 10 sec. The total distance covered by the particle during this time is 30 m. Which of the following statements about the motion of the particle is false

1. Displacement of the particle is zero

2. Average speed of the particle is 3 m/s

3. Displacement of the particle is 30 m

4. Both (a) and (b)

Q.

A train has a speed of 60 km/h for the first one hour and 40 km/h for the next half hour. Its average speed in km/h is

1. 50

2. 53.33

3. 48

4. 70

Q. A man walks on a straight road from his home to a market $2.5km$ away with a speed of $5km/h$. Finding the market closed, he instantly turns and walks back home with a speed of $7.5km/h$. The average speed of the man over the interval of time $0to40min$ is equal to

1. $5km/h$
2. $\frac{25}{4}km/h$
3. $\frac{30}{4}km/h$
4. $\frac{45}{8}km/h$

Q.

A car moves for half of the total time of travel at 80 km/h and for rest half of the time at 40 km/h.

If the total distance covered is 60 km, what is the average speed of the car?

1. 60 km/h

2. 80 km/h

3. 120 km/h

4. 180 km/h

Q. A particle moves on a straight line and its a - t graph is shown.
List - I gives some quantites and List - II gives some possible magnitudes of quantites then correct match is

$\begin{array}{cc}\text{List - I}& \text{List - II}\\ \text{I) Average velocity of 4 sec}& \text{P) 0}\\ \text{II) Average acceleration of 4 sec}& \text{Q) 5}\\ \text{III) Displacement in 4 sec}& \text{R) 10}\\ \text{IV) Velocity at t = 4 sec}& \text{S) 20}\\ & \text{T) 40}\\ & \text{U) 50}\end{array}$

1. $I\to R,II\to Q,III\to T,IV\to S$
2. $I\to S,II\to R,III\to T,IV\to U$
3. $I\to R,II\to Q,III\to U,IV\to T$
4. $I\to R,II\to P,III\to T,IV\to S$