A car starts from rest and moves along x-axis with constant acceleration (5m/secondsquare) fr 8 sec. If it then countinues with constant velocity. What distance will the car cover in 12 sec since it started frm rest. plz anybody explain me
Memorize this:
distance=initialvelocity*time+ 1/2 acceleration*time^2
THE CAR COVERS 7.5M/SECONDSQUARE
10
To find the distance the car will cover in 12 seconds, we need to break down the problem into two parts: the first 8 seconds with constant acceleration and the remaining 4 seconds with constant velocity.
First, let's calculate the distance covered during the first 8 seconds using the formula:
\[ s = ut + \frac{1}{2}at^2 \]
Where:
- s is the distance traveled,
- u is the initial velocity (in this case, 0 m/s since the car starts from rest),
- a is the acceleration (5 m/s²),
- and t is the time taken (8 seconds).
Plugging in the values:
\[ s = 0 * 8 + \frac{1}{2} * 5 * 8^2 \]
\[ s = 0 + \frac{1}{2} * 5 * 64 \]
\[ s = \frac{1}{2} * 5 * 64 \]
\[ s = 2.5 * 64 \]
\[ s = 160 \, \text{meters} \]
Therefore, during the first 8 seconds, the car covers a distance of 160 meters.
Now, for the remaining 4 seconds with constant velocity, we can use the formula:
\[ s = vt \]
Where:
- s is the distance traveled,
- v is the constant velocity (which we need to find),
- and t is the time taken (which is 4 seconds).
Since the velocity remains constant, we can assume it is the same as the final velocity after 8 seconds. To find this final velocity, we can use the formula:
\[ v = u + at \]
Where:
- v is the final velocity,
- u is the initial velocity (which is 0 m/s),
- a is the acceleration (5 m/s²),
- and t is the time taken (which is 8 seconds).
Plugging in the values:
\[ v = 0 + 5 * 8 \]
\[ v = 0 + 40 \]
\[ v = 40 \, \text{m/s} \]
Now, we can find the distance covered during the remaining 4 seconds:
\[ s = 40 * 4 \]
\[ s = 160 \, \text{meters} \]
Therefore, during the next 4 seconds with constant velocity, the car covers an additional distance of 160 meters.
To find the total distance covered in 12 seconds, we simply add the distances covered during both intervals:
Total distance = 160 meters (from the first 8 seconds) + 160 meters (from the next 4 seconds)
Total distance = 320 meters
Hence, the car will cover a distance of 320 meters in 12 seconds since it started from rest.