Question

A rocket test sled accelerates at a constant rate of 25 m/s2 from rest while moving along a straight track. The rocket engine turns off instantly when the sled reaches a speed 37 m/s. The sled then moves freely (acceleration = 0) for a period of 7 s, after which the brakes are automatically applied giving a constant deceleration of -15 m/s2. What is the total distance that the sled moves?

Answer 1

Answer:

332.01 m

Explanation:

The total distance be the $s = s_1+s_2+s_3$

Case : 1 :- Acceleration

u = 0 m/s

v = 37 m/s

a = 25 m/s²

So, Applying equation of motion as:

$v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{37^2-0^2}{2\times 25}\\\Rightarrow s_1=27.38m$

Case : 2 :- No Acceleration

t = 7 s

v = 37 m/s

$s_2=v\times t\\\Rightarrow s=37\times 7\ m\\\Rightarrow s=259\ m$

Case : 3 :- Deceleration

a = -15 m/s²

u = 37 m/s

v = 0 m/s

So, Applying equation of motion as:

$v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-37^2}{2\times -15}\\\Rightarrow s=45.63\ m$

Hence, S = 27.38 + 259 + 45.63 m = 332.01 m