Question

A cyclist going downhill is accelerating at 1. 2 m/s2. If the final velocity of the cyclist is 16 m/s after 10 seconds, what is the cyclist’s initial velocity?.

Answer 1

`\boxed {\boxed {\sf v_i= 4 \ m/s}}`

Step-by-step explanation:

We are asked to find the cyclist's initial velocity. We are given the acceleration, final velocity, and time, so we will use the following kinematic equation.

`v_f= v_i + at`

The cyclist is acceleration at 1.2 meters per second squared. After 10 seconds, the velocity is 16 meters per second.

• 
  `v_f`= 16 m/s
• a= 1.2 m/s²
• t= 10 s

Substitute the values into the formula.

`16 \ m/s = v_i + (1.2 \ m/s^2)(10 \ s)`

Multiply.

`16 \ m/s = v_i + (1.2 \ m/s^2 * 10 \ s)`

`16 \ m/s = v_i + 12 \ m/s`

We are solving for the initial velocity, so we must isolate the variable
`v_i`. Subtract 12 meters per second from both sides of the equation.

`16 \ m/s - 12 \ m/s = v_i + 12 \ m/s -12 \ m/s`

`4 \ m/s = v_i`

The cyclist's initial velocity is 4 meters per second.