Question

g A small car travels up the hill with a speed of v = 0.2 s (m/s) where s is the distance measured from point A in meters. Determine the magnitude of the car’s acceleration when it reaches s = 50 (m) where the road’s radius of curvature is r

Answer 1

Answer:

The magnitude of the acceleration of the car when $s = 50\,m$ is $2\,\frac{m}{s^{2}}$.

Explanation:

The acceleration can be obtained by using the following differential equation:

$a = v \cdot \frac{dv}{ds}$

Where $a$, $v$ and $s$ are the acceleration, speed and distance masured in meters per square second, meters per second and meters, respectively.

Given that $v = 0.2\cdot s$, its first derivative is:

$\frac{dv}{ds} = 0.2$

The following expression is obtained by replacing each term:

$a = 0.2\cdot 0.2\cdot s$

$a = 0.04\cdot s$

The magnitude of the acceleration of the car when $s = 50\,m$ is:

$a = 0.04\cdot (50\,m)$

$a = 2\,\frac{m}{s^{2}}$