Question

a car is travelling with uniform acceleration along a straight road. the road has marker posts every 200m. when the car passed one post, it has a speed of 10ms-2 and when it passes the next one, its speed is 20ms-2. what is the car's acceleration?

Answer 1

A car is travelling with uniform acceleration along a straight road. The road has marker posts every 200m. When the car passed one post, it has a speed of 10ms-2 and when it passes the next one, its speed is 20ms-2. What is the car's acceleration?

$$v _ {1} = 1 0 \frac {m}{s} - \text {initial speed}$$ $$v _ {2} = 2 0 \frac {m}{s} - \text {final speed}$$ $$d = 2 0 0 m - \text {distance}$$

Equation for speed:

$$v _ {2} = v _ {1} + a * t \quad = > \quad t = \frac {v _ {2} - v _ {1}}{a} - \text {time of motion}$$

Equation for distance:

$$S = \frac {v _ {1} + v _ {2}}{2} t$$

Substitute t:

$$S = \frac {v _ {2} ^ {2} - v _ {1} ^ {2}}{2 a}$$

Therefore:

$$a = \frac {v _ {2} ^ {2} - v _ {1} ^ {2}}{2 S} = \frac {2 0 ^ {2} - 1 0 ^ {2}}{2 * 2 0 0} = \frac {3 0 0}{4 0 0} = 0. 7 5 m / s ^ {2}$$

Answer: $a = 0.75 \, \text{m/s}^2$