The acceleration-time graph for a particle is given in the figure. If it starts motion at \(t=0\), the distance travelled in \(3\) s will be:
      
1. \(4~\text{m}\)
2. \(2~\text{m}\)
3. \(0~\text{m}\)
4. \(6~\text{m}\)

Figure shows the position of a particle moving on the x-axis as a function of time

(1) The particle has come to rest 4 times

(2) The velocity at t = 8 s is negative

(3) The velocity remains positive for t = 2 s to t = 6 s

(4) The particle moves with a constant velocity

A particle moves along x-axis in such a way that its x co-ordinate varies with time according to the equation x = 4 - 2t + t². The velocity of the particle will vary with time as-

(1) 

(2) 

(3) 

(4) 

The position (x) of a particle moving along x-axis vares with time (t) as shown in figure. The average acceleration of particle in time interval t=0 to t=8 s is

(1) 3 m/s²

(2) - 5 m/s²

(3) - 4 m/s²

(4) 2.5 m/s²

The position (x)-time (t) graph for a particle moving along a straight line is shown in the figure. The average speed of particle in time interval t=0 to t=8 s is

(1) Zero 

(2) 5 m/s

(3) 7.5 m/s

(4) 9.7 m/s

A boat covers certain distance between two spots in a river taking t₁ hrs going downstream and t₂ hrs going upstream. What time will be taken by boat to cover same distance in still water?

(1) $\frac{t_1+t_2}{2}$

(2) $2\left(t_2-t_1\right)$

(3) $\frac{2t_1{t}_2}{t_1+t_2}$

(4) $\sqrt{t_1{t}_2}$

A train of 150 m length is going towards North a speed of 10 m/s. A bird is flying at 5 m/s parallel to the track towards the South. The time taken by the to the track bird to cross the train is

(1) 10 s

(2) 15 s

(3) 30 s

(4) 12 s

Two cars are moving in the same direction with a speed of 30 km/h. They are separated from each other by 5 km. The third car moving in the opposite direction meets the two cars after an interval of 4 minutes. The speed of the third car is

(1) 30 km/h

(2) 25 km/h

(3) 40 km/h

(4) 45 km/h

Two cars A and B are moving in the same direction with velocities 30 m/s and 20 m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of 2 m/s². There will be no collision when

(1) d < 2.5 m

(2) d > 125 m

(3) d > 25 m

(4) d < 125 m

A ball is dropped from the top of a building of height 80 m. At the same instant, another ball is thrown upwards with a speed 50 m/s from the bottom of the building. The time at which balls will meet is-

(1) 1.6 s

(2) 5 s

(3) 8 s

(4) 10 s