A car is moving on a straight road with uniform acceleration. The following table gives the speed of the car at various instants of time :Speed (m/s) : 5 10 15 20 25 30Time (s) : 0 10 20 30 40 50The distance travelled by the car in 50 seconds.
Question
A car is moving on a straight road with uniform acceleration. The following table gives the speed of the car at various instants of time :Speed (m/s) : 5 10 15 20 25 30Time (s) : 0 10 20 30 40 50The distance travelled by the car in 50 seconds.
Solution
To find the distance travelled by the car in 50 seconds, we can use the formula for distance travelled under uniform acceleration, which is:
d = ut + 0.5at^2
where:
- d is the distance travelled,
- u is the initial speed,
- a is the acceleration, and
- t is the time.
From the table, we can see that the initial speed (u) is 5 m/s and the time (t) is 50 seconds.
To find the acceleration (a), we can use the formula:
a = (v - u) / t
where v is the final speed. From the table, we can see that the final speed (v) is 30 m/s. So, the acceleration is:
a = (30 m/s - 5 m/s) / 50 s = 0.5 m/s^2
Now we can substitute these values into the formula for distance:
d = ut + 0.5at^2 d = (5 m/s * 50 s) + 0.5 * 0.5 m/s^2 * (50 s)^2 d = 250 m + 625 m d = 875 m
So, the car travelled 875 meters in 50 seconds.
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