a car skids to a halt at a rate of -9.4 m/s2. the skid marks measure 34 m. what speed was the car going when it slammed on the brakes?
34 = v^2/18.8
v = 25.28
Hi can you explain how you got the answer
To find the initial speed (v₀) of the car before it slammed on the brakes, we can use the kinematic equation:
v² = v₀² + 2aΔx
Where:
- v is the final velocity (which is 0 m/s because the car skids to a halt),
- v₀ is the initial velocity we want to find,
- a is the acceleration (-9.4 m/s²), and
- Δx is the distance covered (34 m).
Rearranging the equation to solve for v₀:
v₀² = v² - 2aΔx
v₀² = 0 - 2(-9.4)(34)
v₀² = 2(9.4)(34)
v₀² = 2(9.4)(34)
v₀² = 633.6
v₀ = 25.17 m/s
Therefore, the car was going at a speed of approximately 25.17 m/s when it slammed on the brakes.
To find the initial speed of the car when it slammed on the brakes, we can use the formula:
(v^2 - u^2) = 2as
where:
- v = final velocity (0 m/s as the car comes to a halt)
- u = initial velocity (what we need to find)
- a = acceleration (-9.4 m/s^2)
- s = distance covered (34 m)
Substituting the values into the formula, we get:
(0^2 - u^2) = 2(-9.4)(34)
Simplifying further:
-u^2 = 2(-9.4)(34)
-u^2 = -2(9.4)(34)
-u^2 = -2(319.6)
-u^2 = -639.2
Now, solving for u, we take the square root of both sides:
u = √(639.2)
Calculating the square root of 639.2, we find:
u ≈ 25.3 m/s
Therefore, the car's initial speed when it slammed on the brakes was approximately 25.3 m/s.