Question

What constant acceleration in si units must a car have to go from zero to 60 mph in 10s. what fraction of g is this?

Answer 1

The acceleration of the car in SI units is 2.68m/s².

The acceleration is 0.27 times the acceleration due to gravity g.

Convert the speed in mph into m/s.

1 mile = 1609 m and 1h = 3600 s.

Therefore,

`v=((60 miles)/(1 h) )((1609 m)/(1 mile) )((1h)/(3600s)) =26.82m/s`

Acceleration is the rate of change of velocity. The car starts from rest , its initial velocity u = 0 and accelerates to a velocity v of 26.82 m/s in 10 s.

Use these values in the equation and calculate the acceleration.

`a=(v-u)/(t) \\ =((26.82 m/s)-(0m/s))/(10s) \\ =2.682 m/s^2`

Thus the car accelerates at a rate of 2.68 m/s².

The acceleration due to gravity g on Earth has a value 9.81 m/s².

Find the ratio
`(a)/(g)`

`(a)/(g) =(2.682m/s^2)/(9.81m/s^2) \\ =0.27 a=0.27g`

The car's acceleration is 0.27 times the value of g.