If a car starts from rest and travels for 5.0 seconds with a uniform acceleration of +1.5 m/s2. The driver then applies the brakes for 3.0 seconds, causing a uniform acceleration of - 2.1 m/s2.
and?
7.5 m/s
qws
To answer this question, we need to use the equations of motion.
1. First, let's calculate the initial velocity of the car before it starts accelerating. Since the car starts from rest (zero initial velocity), its initial velocity (u) is 0 m/s.
2. Next, let's calculate the distance traveled by the car during the first phase when it accelerates for 5.0 seconds with a uniform acceleration of +1.5 m/s^2. We can use the equation:
distance (s) = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)^2
Substituting the given values:
s = 0 * 5.0 + 0.5 * 1.5 * (5.0)^2
= 0 + 0.5 * 1.5 * 25.0
= 0 + 0.75 * 25.0
= 0 + 18.75
= 18.75 meters
Therefore, during the first phase, the car travels a distance of 18.75 meters.
3. After the first phase, the car applies the brakes for 3.0 seconds, causing a uniform deceleration (negative acceleration) of -2.1 m/s^2. We can use the same equation to calculate the distance traveled during this phase:
s = initial velocity (u) * time (t) + 0.5 * acceleration (a) * time (t)^2
Since the car stops at the end, the final velocity (v) is 0 m/s. The initial velocity (u) can be found using the equation:
final velocity (v) = initial velocity (u) + acceleration (a) * time (t)
Rearranging the equation, we get:
initial velocity (u) = final velocity (v) - acceleration (a) * time (t)
u = 0 - (-2.1) * 3.0
= 0 + 6.3
= 6.3 m/s
Now, let's calculate the distance traveled during the braking phase:
s = 6.3 * 3.0 + 0.5 * (-2.1) * (3.0)^2
= 18.9 - 0.5 * 2.1 * 9.0
= 18.9 - 0.5 * 18.9
= 18.9 - 9.45
= 9.45 meters
Therefore, during the braking phase, the car travels a distance of 9.45 meters.
4. Finally, to find the total distance covered by the car, we add the distances traveled during both phases:
Total distance = distance during first phase + distance during braking phase
= 18.75 + 9.45
= 28.20 meters
Therefore, the total distance covered by the car is 28.20 meters.