Question

A boat is traveling along a circular curve having a radius of 100 ft. If its speed at t = 0 is 15 ft>s and is increasing at v # = (0.8t) ft>s 2 , determine the magnitude of its acceleration at the instant t = 5 s.

Answer 1

Answer:

a=7.42 ft/s²

Explanation:

Given data

Radius r=100 ft

Speed v=15 ft/s at t=0

acceleration a₁=(0.8t) ft/s²

To find

acceleration a

solution

As acceleration is first derivative of velocity with respect to time

So

$a=\frac{dV}{dt}\\ dV=a.dt\\integrate\\\int\limits{} \, dv=\int\limits{a} \, dt\\v-v_{o} =\int\limits{0.8t} \, dt\\v-15=0.4t^{2}\\ v=0.4t^{2}+15\\ at\\t=5s\\v=0.4(5)^{2}+15\\v=25ft/s$

As

$velocity=distance/time\\time=distance/velocity\\time=100ft/25ft/s\\time=4s$

a₂=v/t

a₂=(25ft/s)/4s

a₂=6.25 ft/s²

$a=\sqrt{(6.25)^{2}+(0.8*5)^{2} }\\ a=7.42 ft/s^{2}$