Question

1. A train, initially at rest, is subject to an acceleration of 32 m/s2.  How long will it take for that object to travel 3100 m?

Formula:  x = x0 + v0t + ½ at2

 

1. A bowling ball is at rest when it undergoes a constant acceleration of 13 m/s2 for 5 s.  How far will it have traveled during this time?

Formula:  x = x0 + v0t + ½ at2

1. What is the velocity of a dropped object after it has fallen for 2.0s?

Formula: v  = v0 +gt  

1. A ball is thrown straight up from the ground with an unknown velocity. It reaches its highest point after 3.5 s. With what initial velocity did it leave the ground? 

Formula:  v0  = v -gt

Answer 1

a. The time can be found from the following equation:

$$3100=0+0·t+32·t^2/2,\\ t=\sqrt{3100·2/32}=13.9\text{ s}.$$

b. The distance is

$$x=0+0·5+13·5^2/2=162.5\text{ m}.$$

c. The velocity is

$$v=0+9.8·2=19.6\text{ m/s}.$$

d. The initial velocity:

$$v_0=0-9.8·3.5=34.3\text{ m/s}.$$