A car is traveling at 72 km/hr. The driver begins to apply the brakes and the begins to slow with a constant acceleration (a). After the brakes are applied, the car stops in a distance of 100 m. What is the acceleration?
My teacher gave the class a list of formulas but didn't really go over them with some examples. I still wondering on what formula to use.
A car is traveling in the +x direction. The driver applies the brakes and slows down. The acceleration is in the —— direction. -x, -y, +z, +x, 0
To solve this problem, you can use the formula for calculating the distance traveled during uniformly accelerated motion:
d = (v^2 - u^2) / (2a),
where:
d is the distance traveled,
v is the final velocity,
u is the initial velocity, and
a is the acceleration.
In this case, the car starts with an initial velocity of 72 km/hr, which needs to be converted to m/s for consistency with the units. To convert km/hr to m/s, divide the velocity by 3.6:
u = 72 km/hr ÷ 3.6 = 20 m/s.
The final velocity, v, is 0 m/s because the car comes to a stop.
The distance traveled, d, is given as 100 m.
Now, substituting the known values into the formula, we have:
100 = (0^2 - 20^2) / (2a).
Simplifying further:
100 = -400 / (2a).
To get the value of a, we need to solve for it. Rearranging the equation:
2a = -400 / 100,
2a = -4,
a = -2 m/s^2.
Therefore, the acceleration of the car during braking is -2 m/s^2. The negative sign indicates that the car is decelerating.