A car is travelling at 20 m/s along a road A child runs out into the road 50 m ahead and the driver steps on the break pedal What must be the cars deceleration be if the car stops just before it reaches the chid
the average speed during deceleration will be 10 m/s
it takes 5 seconds to travel 50 meters at that average speed, so
1/2 at^2 = 50
a = 100/25 = 4 m/s^2
To find the required deceleration of the car, we need to consider the initial velocity of the car, the distance between the car and the child, and the final velocity (zero in this case) when the car stops just before reaching the child.
Here's how we can calculate the deceleration:
Step 1: Identify the given information:
- Initial velocity (vi) of the car = 20 m/s
- Distance between the car and the child (d) = 50 m
- Final velocity (vf) of the car = 0 m/s
Step 2: Use the kinematic equation to find the deceleration (a) of the car:
vf^2 = vi^2 + 2ad
Since the final velocity (vf) is zero, the equation becomes:
0 = vi^2 + 2ad
Rearranging the equation, we get:
2ad = -vi^2
Step 3: Substitute the known values into the equation:
2a(50 m) = -(20 m/s)^2
Step 4: Solve for the deceleration (a):
a = - (20 m/s)^2 / (2 * 50 m)
a = -400 m^2/s^2 / 100 m
a = -4 m/s^2
Hence, the car's deceleration must be 4 m/s^2 in order to stop just before reaching the child. Note that the negative sign indicates that the car is decelerating, or slowing down.