A car start from rest and affairs a velocity of 40m/s in 20s. If maintain this velocity for 30s and then comes to rest in 25s. Calculate the total distance travelled
To calculate the total distance traveled, we need to find the distance covered during each phase of the car's motion and then sum them up.
Phase 1: Acceleration phase
Initial velocity, u = 0 m/s
Final velocity, v = 40 m/s
Time, t = 20 s
Using the equation of motion: v = u + at
40 = 0 + a * 20
a = 40/20
a = 2 m/s²
Using the equation of motion: s = ut + (1/2)at²
s = 0 * 20 + (1/2) * 2 * (20)²
s = 0 + 0.5 * 2 * 400
s = 0 + 0.5 * 800
s = 0 + 400
s = 400 m
Phase 2: Constant velocity phase
Velocity, v = 40 m/s
Time, t = 30 s
Since the velocity is constant, the distance covered is given by:
s = v * t
s = 40 * 30
s = 1200 m
Phase 3: Deceleration phase
Initial velocity, u = 40 m/s
Final velocity, v = 0 m/s
Time, t = 25 s
Using the equation of motion again: v = u + at
0 = 40 + a * 25
a = -40/25
a = -1.6 m/s²
Using the equation of motion: s = ut + (1/2)at²
s = 40 * 25 + (1/2) * (-1.6) * (25)²
s = 1000 - 20 * 25²
s = 1000 - 20 * 625
s = 1000 - 12500
s = -11500 m
Since distance cannot be negative, the distance covered during the deceleration phase is 0 m.
Now, we can calculate the total distance traveled:
Total distance = Phase 1 distance + Phase 2 distance + Phase 3 distance
Total distance = 400 m + 1200 m + 0 m
Total distance = 1600 m
Therefore, the car traveled a total distance of 1600 meters.