A car starts from rest and its velocity reaches 24 m s⁻¹ in 6 s. Find the average acceleration and the distance travelled in these 6 s.
Given: Initial velocity (u) = 0 m s⁻¹, Final velocity (v) = 24 m s⁻¹, Time (t) = 6 s. Using the formula for average acceleration: a = (v - u) / t a = (24 m s⁻¹ - 0 m s⁻¹) / 6 s = 4 m s⁻²
Find the distance travelled in these 6 s.
The distance travelled can be calculated using the equation of motion s = ut + ½at² (or by finding the area under the velocity-time graph). s = () + ½ × 4 m s⁻² × (6 s)² s = 0 + = 72 m
Explanation
The average acceleration is calculated using the formula a = (v - u) / t, as demonstrated in Example 4.3 of the text. The distance travelled under constant acceleration is found using the kinematic equation s = ut + ½at², which is equivalent to calculating the area under the velocity-time graph (a triangle with base 6 s and height 24 m s⁻¹), a method referenced in the text for finding displacement.