A car is traveling at a speed of 30.m^-1 when a traffic light,40 ahead turns red.the driver take 1 second to react ( reaction time) before he slams on the brakes.The car stopped within 2 seconds. Will the car stop at traffic light? Show by calculation
The acceleration applied was -15m/s^2, since 30m/s was reduced to zero in 2 seconds.
So, the total distance traveled during braking was
s = 30*2 - 1/2 * 15 * 2^2
add to that the 30m moved before hitting the brakes
To determine if the car will stop at the traffic light, we need to calculate the distance it covers during the reaction time and the distance it covers while braking.
Given:
Initial speed (u) = 30 m/s
Reaction time (t1) = 1 second
Braking time (t2) = 2 seconds
First, let's calculate the distance covered during the reaction time. The formula for distance covered (s) is given by:
s = u * t
During the reaction time, the car continues moving at a constant velocity, so the distance covered is:
s1 = 30 m/s * 1 s
s1 = 30 m
Now, we need to calculate the distance covered while braking. To do this, we need to determine the car's deceleration or negative acceleration.
Since we know the initial speed (u), final speed (v) = 0 m/s (as the car is coming to a stop), and time taken (t2) = 2 seconds, we can use the following equation of motion:
v = u + at
Since the final speed (v) is 0 m/s, the equation becomes:
0 = 30 m/s + a * 2 s
Solving for acceleration (a), we get:
-30 m/s = 2a
a = -15 m/s² (negative because it is deceleration)
Now, we can calculate the distance covered while braking using the equation of motion:
s2 = ut + (1/2)at^2
s2 = 30 m/s * 2 s + (1/2) * (-15 m/s²) * (2 s)^2
s2 = 60 m - 60 m
s2 = 0 m
Therefore, the distance covered while braking (s2) is 0 m, meaning the car will stop exactly where the traffic light is located.