Motion in Straight Line

A motorboat covers a given distance in 6 h moving downstream on a river. It covers the same distance in 10 h moving upstream. The time it takes to cover the same distance in still water is

• 9 h

• 7.5 h

• 6.5 h

• 8 h

The displacement-time graph of two moving particles make angles of 30° and 45° with the X-axis. The ratio of their velocities is

• $\sqrt{3} : 2$

• 1 : 1

• 1 : 2

• $1 : \sqrt{3}$

In a lift moving up with an acceleration of 5ms^-2 dropped from a height of 1.25 m. The time taken by the ball to reach the floor of the lift is (g = 10 ms^-2)

• 0.3 s

• 0.2 s

• 0.16 s

• 0.4 s

A car moves from A to B with a speed of 30 km/h and from B to A with a speed of 20 km/h. What is the average speed of the car ?

• 25 km/h

• 24 km/h

• 50 km/h

• 10 km/h

A body starts from rest and moves with constant acceleration for t sec. It travels a distance x₁ in first half of time and x₂ in next half of time, then

• x₂ = x₁

• x₂ = 2x₁

• x₂ = 3x₁

• x₂ = 4x₁

The velocity-time graph for two bodies A and B are shown in figure. Then, the acceleration of Aand B are in the ratio

• sin 25° to sin 50°

• tan 25° to tan 40°

• cos 25° to cos 50°

• tan 25° to tan 50°

A body falls freely for 10 s. Its average velocity during this journey is (Take, g = 10 ms^-2)

• 100 ms^-1

• 10 ms^-1

• 50 ms^-1

• 5 ms^-1

From the top of a tower a stone is thrown up which reaches the ground in a time t₁. A second stone thrown down with the same speed reaches the ground in a time t₂. A third stone released from rest from the same between reaches the ground in a time t₃. Then

• $\frac{1}{{\mathrm{t}}_3} = \frac{1}{{\mathrm{t}}_2} - \frac{1}{{\mathrm{t}}_1}$

• ${\mathrm{t}}_3^2 = {\mathrm{t}}_1^2 - {\mathrm{t}}_2^2$

• ${\mathrm{t}}_3 = \frac{{\mathrm{t}}_1 + {\mathrm{t}}_2}{2}$

• ${\mathrm{t}}_3 = \sqrt{{\mathrm{t}}_1 {\mathrm{t}}_2}$