Question

A ball is rolled up a ramp with an initial velocity of +6.0m/s. The ball experiences an acceleration of -2.0m/s^2. How can we determine at what time(s) the ball is +5.0m from its initial position on the ramp?

Answer 1

• Initial velocity=u=6m/s
• Acceleration=a=-2m/s^2
• Distance=s=5m
• Time is t

Apply second equation of kinematics

`\\ \tt\hookrightarrow s=ut+(1)/(2)at^2`

`\\ \tt\hookrightarrow 5=6t+(1)/(2)(-2)t^2`

`\\ \tt\hookrightarrow 6t-t^2=5`

`\\ \tt\hookrightarrow t^2-6t+5=0`

`\\ \tt\hookrightarrow t^2-5t-t+5=0`

`\\ \tt\hookrightarrow t(t-5)-1(t-5)=0`

`\\ \tt\hookrightarrow (t-1)(t-5)=0`

`\\ \tt\hookrightarrow t=(1,5)`