A car travelling at 18 km/h increases its velocity to 48 km/h in 6 seconds. What is the acceleration in metres per second squared?

To determine the acceleration of the car, we first need to understand the relationship between acceleration, initial velocity, final velocity, and time. Acceleration is defined as the change in velocity over the time it takes for that change to occur. The formula for acceleration (a) can be expressed as:

[ a = \frac{v_f - v_i}{t} ]

where ( v_f ) is the final velocity, ( v_i ) is the initial velocity, and ( t ) is the time taken for the change in velocity.

In this case, the initial velocity ( v_i ) is 18 km/h, and the final velocity ( v_f ) is 48 km/h. To calculate acceleration, we first convert these velocities from kilometers per hour to meters per second, as the final unit for acceleration needs to be in meters per second squared.

To convert km/h to m/s, we use the conversion factor ( 1 \text{ km/h} = \frac{1}{3.6} \text{ m/s} ):

• Initial velocity: ( 18 \text{ km/h} \times \frac{1}{3.6} = 5 \text{ m/s