A driver takes to apply the brake after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of and the brakes cause a deceleration of . Find the distance traveled by car after he sees the need to put the brakes on.
Step 1: Given
Reaction time:
Initial velocity of car:
Final velocity of car: (as it comes to rest)
Acceleration: (since, it is deceleration)
Step 2: Formula Used
Distance is the product of speed and time, .
According to the third equation of motion, , where is final velocity, is initial velocity, is acceleration and is displacement.
Step 3: Calculate the distance travelled by car in reaction time.
Calculate the initial velocity of car in meters per second by multiplying it by .
Calculate the distance travelled by car in reaction time.
.
Step 4: Calculate the total distance travelled by car
Calculate the distance travelled by car after the driver realizes the need to put the brakes on.
.
Calculate the total distance travelled by car by adding both the distances.
Hence, the total distance travelled by car is .