Question

Imagine a car traveling around a circular track at a speed of 35 mph and with a centripetal acceleration with a magnitude of 2.0 m/s2. Of the car's speed is doubled to 70 mph, what magnitude of centripetal acceleration will it have?

Answer 1

When the car's speed is doubled centripetal acceleration is 8 m/s²

Step-by-step explanation:

We know the equation for centripetal acceleration

`a=(v^2)/(r)`

where v is the linear velocity and r is the radius.

So we have

a ∝ v²

`(a_1)/(a_2)=(v_1^2)/(v_2^2)`

Given that

a₁ = 2 m/s²

v₁ = 35 mph

v₂ = 70 mph

Substituting

`(a_1)/(a_2)=(v_1^2)/(v_2^2)\\\\(2)/(a_2)=(35^2)/(70^2)\\\\(2)/(a_2)=(1)/(2^2)\\\\a_2=4* 2\\\\a_2=8m/s^2`

When the car's speed is doubled centripetal acceleration is 8 m/s²