A car starts from rest and attains a velocity of 40 metres per second in 20 seconds. it maintains this velocity for 30 seconds and then comes to rest in 25 seconds.
Calculate the total distance covered by the body
http://www.jiskha.com/display.cgi?id=1478031138
first 20 seconds
d=vaverage*time= 20m/s * 20 sec=400m
next 30 seconds
d= 40*30=1200 m
last 25 seconds
d= avgvelocity*time
= 20*25=500m
total distance: add them
I have answered this three times now.
To calculate the total distance covered by the car, we need to split the motion into three phases:
1. Acceleration phase: The car starts from rest and attains a velocity of 40 m/s in 20 seconds.
2. Constant velocity phase: The car maintains a velocity of 40 m/s for 30 seconds.
3. Deceleration phase: The car comes to rest in 25 seconds.
Let's calculate the distance traveled in each phase:
1. In the acceleration phase, we can use the equation:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Since the car starts from rest, the initial velocity (u) is 0. The final velocity (v) is 40 m/s, and the time (t) is 20 seconds. The acceleration (a) can be found using the formula:
acceleration = (final velocity - initial velocity) / time
Plugging in the values:
acceleration = (40 - 0) / 20
acceleration = 2 m/s^2
Now, we can calculate the distance:
distance = (0 * 20) + (0.5 * 2 * 20^2)
distance = 0 + (0.5 * 2 * 400)
distance = 0 + 400
distance = 400 meters
2. In the constant velocity phase, the car maintains a velocity of 40 m/s for 30 seconds. Since the velocity remains constant, the distance traveled can be calculated using the formula:
distance = velocity * time
distance = 40 * 30
distance = 1200 meters
3. In the deceleration phase, the car comes to rest in 25 seconds. The initial velocity (u) is 40 m/s, the final velocity (v) is 0, and the time (t) is 25 seconds. Assuming constant deceleration, we can use the formula:
distance = (initial velocity * time) - (0.5 * acceleration * time^2)
Here, the initial velocity is 40 m/s, and the final velocity is 0 m/s. We need to find the acceleration using the formula:
acceleration = (final velocity - initial velocity) / time
acceleration = (0 - 40) / 25
acceleration = -1.6 m/s^2 (negative because it's deceleration)
Now, we can calculate the distance:
distance = (40 * 25) - (0.5 * -1.6 * 25^2)
distance = 1000 + (0.5 * 1.6 * 625)
distance ≈ 1000 + 500
distance ≈ 1500 meters
Finally, to get the total distance covered by the car, we add the distances from each phase:
Total distance = distance in acceleration phase + distance in constant velocity phase + distance in deceleration phase
Total distance = 400 + 1200 + 1500
Total distance = 3100 meters
Therefore, the total distance covered by the car is 3100 meters.