Question

A cart is released from rest at the top of a long ramp at time $t=0$ seconds and moves down the ramp at a constant acceleration rate. At a time of t, the cart has moverd $20cm$ from the top of the ramp. How far will the cart be located from the top of the ramp at the time of $3t$?

• A. $40cm$
• B. $60cm$
• C. $120cm$
• D. $180cm$

Answer 1

The correct option is D $180cm$

Initial speed of the cart $u=0$ m/s

Distance covered by cart after time $t$ $S=20$ cm

Using $S=ut+\frac{1}{2}a{t}^2$

$\therefore$ $20=0+\frac{1}{2}a{t}^2$ $⟹a{t}^2=40$

Distance covered by cart in time $3t$ $S^{\prime }=u{t}^{\prime }+\frac{1}{2}a(t^{\prime }{)}^2$ where $t^{\prime }=3t$

$\therefore$ $S^{\prime }=0+\frac{1}{2}a(3t{)}^2=0+\frac{9}{2}\times 40=180$ cm