Question

will the acceleration of a car with the same when the car travels around a sharp curve at a constant 60km/hr as when it travels around a gentle curve at the same speed explain?

Answer 1

Speed and velocity use exactly the same units.
So it is perfectly acceptable to say "a car travels around a sharp curve a 60 km/hr".

Restated, what we are saying is that the car moves around a curve at constant speed of 60 km/hr. The statement above does not include directional information.

(However, suppose we said "a car travels around a sharp curve with constant velocity of 60 km/hr". Then, clearly this would be wrong. Velocity does change as it goes around the curve.)

Secondly, let us recall some basic facts of 'Uniform Circular Motion'
An object that travels with Uniform Circular Motion has:
- constant speed
- changing velocity
- acceleration towards the centre

Now, the car in question displays uniform circular motion. This is so even though we are considering a partial circular path.

So, we can use this import formula (you should memorise it)

ar = v ^2 /r

This relates the centripetal acceleration, ar, to the radius of the circle (or in the case of a partial circle, the radius of curvature), r.

From the formula you can see that a sharp bend, i.e. a small r, will give a larger value of centripetal acceleration compared to a gentle bend, i.e a large r.

Substitute v=60 and different values of r into the formula above to verify this.