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.

Respuesta :

Answer:

a) 8 m/s²

b) 100 m

Explanation:

The acceleration of the train can be calculated as

[tex]a=\frac{v_f-v_i}{t}[/tex]

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:

[tex]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[/tex]

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

[tex]x=v_it+\frac{1}{2}at^2[/tex]

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

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

Therefore, the distance traveled by train was 100 m.