Question

One - Dimensional Kinematics

1. A ripe mango, hanging from a branch, suddenly falls down to the ground. If the mango acquired a final velocity of 8 m/s when it hit the ground?

2. If a ball is released to fall down from the top of a building 30 meters high, how many seconds will it take for the ball to reach the ground?

3. Find the time it takes to travel 30 km for a bus which accelerates uniformly from 40km/hr to 80 km/hr.

4. A car initially running at 5 m/s uniformly speeds up to 9 m/s over 20 seconds. What is its acceleration?

5. Timothy drives 10 km to the South and then 20 km to the East. What is the magnitude and direction of his displacement from the origin?

Answer 1

1) The time is

$$t=\frac vg=0.816\text{ s}.$$

2) The time is

$$t=\sqrt{2h/g}=2.47\text{ s}.$$

3) The time is

$$t=\frac{d}{v_\text{avg}}=0.5\text{ h}.$$

4) The acceleration is

$$a=\frac{\Delta v}{t}=0.2\text{ m/s}.$$

5) The magnitude and direction are

$$|r|=\sqrt{10^2+20^2}=22.4\text{ km},\\\space\\ \theta=\arctan\frac{20}{10}=63.4° \text{ S of E}$$