Question

A car sitting at a red light begins to accelerate at 2.0 m/s2 when the light turns green. It continues with this acceleration until it reaches a speed of 20 m/s. It then travels at this speed for another few minutes. How far does the car travel in the first 46 s after the light changes to green?

Answer 1

Answer:

$d = 820 m$

Explanation:

here we know that car starts from rest and continue to accelerate till it will reach to maximum speed of 20 m/s

so we will have

$v_f - v_i = at$

$20 - 0 = 2t$

$t = 10 s$

so car will accelerate till t = 10 then it will move with uniform speed

so the distance moved by the car till it accelerates is given as

$d = \frac{1}{2}at^2$

$d = \frac{1}{2}(2)(10^2)$

$d_1 = 100 m$

now it will move with uniform speed for next 36 s

so we have

$d_2 = 20(36) = 720 m$

so total distance moved by the car is given as

$d = d_1 + d_2$

$d = 100 + 720$

$d = 820 m$

Answer 2

The distance that the car travels in the first 46 s after the light changes to green is; 820 m

Distance time graph

We are given the acceleration as 2 m/s².

Now, we are told that final speed is 20 m/s.

Initial speed is zero since it began at rest.

Using Newton's first equation of motion, we have;

v - u = at

Thus;

20 - 0 = 2t

2t = 20

t = 10 s

Using Newton's equation of motion we have;

S = ut + ½at²

Thus,distance travelled during this 10 seconds is;

S = ½ × 2 × 10²

S = 100 m

Total time throughout is 46 seconds.

Thus, remaining time after 10 seconds is 36 seconds.

Thus, distance for the remaining 36 seconds is;

D = speed × time

D = 20 × 36

D = 720 m

Thus, total distance travelled is;

100 + 720 = 820 m

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