Question

A ball starts from rest and rolls down a hill with uniform acceleration, traveling 150 m during the second 5.0 s of its motion. How far did it roll during the first 5.0 s of motion?

Answer 1

Answer:

50 m

Explanation:

Speed of ball during 1st five seconds of motion = v₁

Initial speed of the ball = u

$v_1=u+at\\\Rightarrow v_1=5a$

Speed of ball during 2nd five seconds of motion = v₂

Initial speed of ball during 2nd five seconds of motion = final Speed of ball during 1st five seconds of motion

$v_2=u+at\\\Rightarrow v_2=5a+5a\\\Rightarrow v_2=10a$

Distance travelled during 2nd five seconds of motion

$\frac{v_1+v_2}{2}\times 5=150\\\Rightarrow 5a+10a=60\\\Rightarrow a=\frac{60}{15}\\\Rightarrow a=4\ m/s^2$

Distance travelled during 1st five seconds of motion

$s=ut+\frac{1}{2}at^2\\\Rightarrow s=0t+\frac{1}{2}4\times 5^2\\\Rightarrow s=50\ m$

∴ Distance travelled during 1st five seconds of motion is 50 m