Question

Help me to solve this.

An automobile, the speed of which is increasing at a rate of 6.​​​0 m/s2, travels along a circular road of radius 20m. When the instantaneous speed of the automobile is 4m/s find (a) the tangential acceleraction components and (b) the magnitude and direction of the total acceleraction​​​​​​​​​​​​​​​

Answer 1

Step-by-step explanation:

The tangential acceleration is given as 6.0 m/s². The radial (centripetal) acceleration is:

ac = v² / r

ac = (4.0 m/s)² / 20 m

ac = 0.80 m/s²

The total acceleration therefore has a magnitude of:

a² = at² + ac²

a² = (6.0 m/s²)² + (0.80 m/s²)²

a = 6.1 m/s²

And the direction (relative to the tangential direction) is:

θ = atan(ac / at)

θ = atan(0.80 m/s² / 6.0 m/s²)

θ = 7.6°