Question

PLEASE HELP and show work, thank you !!

-The top speed of a Utahraptor is about 9 m/s. How long would it take a Utahraptor to run 1500 m if it accelerates from rest to 9 m/s? Assume acceleration is constant and it reaches its top speed at exactly 1500 m from its starting point.

Answer 1

2.94 s

Step-by-step explanation:

v = u + at

where:

v = final velocity = 9 m/s

u = initial velocity = 0 m/s (rest)

a = acceleration

t = time taken to reach final velocity

We can rearrange the equation to solve for time:

t = (v - u) / a

Substituting the given values, we get:

t = (9 m/s - 0 m/s) / a

Now, we need to find the acceleration. We can use another kinematic equation:

s = ut + (1/2)at^2

where:

s = displacement = 1500 m

u = initial velocity = 0 m/s

a = acceleration

t = time taken to cover the displacement

We can rearrange the equation to solve for acceleration:

a = 2(s - ut) / t^2

Substituting the given values, we get:

a = 2(1500 m - 0 m) / (1500 m / 9 m/s)^2

Simplifying, we get:

a = 3.06 m/s^2

Now, we can substitute this value of acceleration in the earlier equation to find the time taken:

t = (9 m/s - 0 m/s) / 3.06 m/s^2

Simplifying, we get:

t = 2.94 s