A car starting from rest is uniformly accelerated so that it's velocity in 5 seconds is 36 km/h . It travels at this velocity for 5 seconds, and then a brake is applied to bring it to rest in the next 5 seconds. Find the total distance travelled
36 km/hr = 10 m/s
so, the acceleration is
a = (10m/s) / (5s) = = 2 m/s^2
distance covered in 1st 5 seconds:
s = 1/2 at^2 = 25m
at 10 m/s, it travels another 10*5 = 50 m
the distance braking is the same as the first 25m, so the total distance is 100m
It is amazing and very helpful and very informative and very complex and I do not understand
To find the total distance traveled by the car, we need to consider the three phases of its motion: acceleration, uniform motion, and deceleration.
Phase 1: Acceleration
We have the initial velocity as 0 (starting from rest) and the final velocity after 5 seconds as 36 km/h. To find the acceleration, we need to convert the final velocity to meters per second (m/s).
1 km/h = 1000 m / 3600 s
36 km/h = 36 * (1000/3600) m/s = 10 m/s
Using the equation of motion:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can rearrange it to solve for acceleration:
a = (v - u) / t
a = (10 m/s - 0) / 5 s
a = 2 m/s²
Phase 2: Uniform Motion
The car travels at a constant velocity of 10 m/s for 5 seconds. The distance covered in this phase can be calculated using the equation:
Distance = Velocity * Time
Distance = 10 m/s * 5 s
Distance = 50 meters
Phase 3: Deceleration
The car comes to rest in the next 5 seconds. The acceleration during deceleration is equal to the negative of the acceleration during acceleration.
a = -2 m/s²
Using the equation of motion:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can rearrange it to solve for final velocity:
v = u + at
0 = 10 m/s + (-2 m/s²) * t
2t = 10
t = 5 s
So, it takes 5 seconds for the car to come to rest during deceleration.
The distance covered during deceleration can be calculated using the equation:
Distance = Initial Velocity * Time + 0.5 * Acceleration * Time²
Distance = 10 m/s * 5 s + 0.5 * (-2 m/s²) * (5 s)²
Distance = 50 meters - 25 meters
Distance = 25 meters
Total Distance Traveled:
The total distance traveled by the car is the sum of the distances covered in each phase:
Total Distance = Distance during acceleration + Distance during uniform motion + Distance during deceleration
Total Distance = 0 + 50 + 25
Total Distance = 75 meters
Therefore, the total distance traveled by the car is 75 meters.