A car starts from rest and moves along the x-axis with constant acceleration 5 m s–2 for 8 seconds. If it then continues with constant velocity, what distance will the car cover in 12 seconds since ?

To find the distance covered by the car in 12 seconds, we need to break down the motion into two parts: the first 8 seconds with constant acceleration and the next 4 seconds with constant velocity.

1. Calculate the distance covered during the first 8 seconds with constant acceleration:
Using the equation of motion:
s = ut + (1/2)at^2
where:
s = distance covered
u = initial velocity (0 m/s as the car starts from rest)
a = acceleration (5 m/s^2)
t = time (8 seconds)

s = 0 + (1/2)(5)(8)^2
s = 0 + (1/2)(5)(64)
s = 0 + 160
s = 160 meters

2. Calculate the distance covered during the next 4 seconds with constant velocity:
Since the car continues with constant velocity after the initial 8 seconds, the distance covered during the next 4 seconds can be calculated using the formula:
s = vt
where:
v = constant velocity (which is the final velocity after the initial 8 seconds)
t = time (4 seconds)

To find the final velocity after 8 seconds, we use the equation:
v = u + at
where:
u = initial velocity (0 m/s)
a = acceleration (5 m/s^2)
t = time (8 seconds)

v = 0 + (5)(8)
v = 40 m/s

Now, calculate the distance covered during the next 4 seconds:
s = (40)(4)
s = 160 meters

3. Add the distances covered in the two parts to find the total distance covered in 12 seconds:
Total distance = distance covered in the first 8 seconds + distance covered in the next 4 seconds
Total distance = 160 + 160
Total distance = 320 meters

Therefore, the car will cover a distance of 320 meters in 12 seconds since starting from rest.

Step 1: Calculate the distance covered during the accelerated motion

Distance = (1/2) - acceleration - time^2
= (1/2) - 5 - (8)^2
= 160 m

Step 2: Calculate the time spent at constant velocity

Total time = 12 s
Time spent in accelerated motion = 8 s
Therefore, time spent at constant velocity = 12 - 8 = 4 s

Step 3: Calculate the distance covered during the constant velocity motion

Distance = velocity - time
Velocity = acceleration - time
Velocity = 5 - 8 = 40 m/s
Distance = 40 - 4 = 160 m

Step 4: Add the distances covered in both motions

Total distance = 160 m (accelerated) + 160 m (constant velocity)
= 320 m

Therefore, the car will cover a distance of 320 m in 12 seconds since it started from rest.