Question

You're driving at speed v0 when you spot a stationary moose on the road, a distance d ahead. Find an expression for the magnitude of the minimum constant acceleration you need if you're to stop before hitting the moose. Note: be careful when inputting the square of a variable that has a subscript. For example, the square of v0 should be entered v02 . Don't enter v20 or v02 ! Feel free to use parenthesis to make sure your answer is interpreted correctly. Express your answer in terms of the variables v0 and d. a=

Answer 1

Initial distance of the moose from you = d

Your initial speed = V₀

Your final speed = V₁ = 0 m/s (Stops before hitting the moose)

Your acceleration = a

For minimum acceleration you need to come to rest just before the moose that is you to come to rest by traveling a distance 'd'.

(V₁)² = (V₀)² + 2ad

(0)² = (V₀)² + 2ad

The negative sign indicates that it is deceleration as you are slowing down.

We are asked for the magnitude of the acceleration therefore it will be positive.

Your magnitude of minimum acceleration to stop just before hitting the moose is given by,