Question

A train accelerates uniformly from rest to a velocity of 40 m s^-1, in 5 seconds.a)Find the acceleration of the train during the 5 seconds.b) Find the distance travelled by the train during the 5 seconds.

Answer 1

a) 8 m/s²

b) 100 m

Step-by-step explanation:

The acceleration of the train can be calculated as

`a=(v_f-v_i)/(t)`

Where vf is the final velocity, vi is the initial velocity, and t is the time. Replacing vf = 10 m/s, vi = 0 m/s, and t = 5 s, we get:

`a=\frac{40\text{ m/s - 0 m/s}}{5\text{ s}}=\frac{40\text{ m/s}}{5\text{ s}}=8\text{ m/s}^2`

Then, the distance traveled can be calculated using the following equation

`x=v_it+(1)/(2)at^2`

Replacing vi = 0 m/s, t = 5 s, and a = 8 m/s², we get

`\begin{gathered} x=(0\text{ m/s\rparen\lparen5 s\rparen + }(1)/(2)(\text{ 8 m/s}^2)(5\text{ s\rparen}^2 \\ x=0\text{ m + }(1)/(2)(8\text{ m/s}^2)(25\text{ s\rparen} \\ x=0\text{ m+100 m} \\ x=100\text{ m} \end{gathered}`

Therefore, the distance traveled by train was 100 m.