a car travels at uniform velocity of 20m/s for 5 seconds, the breaks are then applied and the car comes to rest with uniform retardation in further 8 seconds. draw a graph of velocity against time.How far does the car travel after the breaks are applied.?
They are brakes.
after 5 sec at constant v
Vi = 20
v = 20 + a t where t is total time - 5
v = 0 when t = 8 so
0 = 20 + a (8)
a = -20/8 = - 5/2
so
v = 20 - (5/2) t = 20 - (5/2)(time - 5)
68.75m
They are brakes.
after 5 sec at constant v
Vi = 20
v = 20 + a t where t is total time - 5
v = 0 when t = 8 so
0 = 20 + a (8)
a = -20/8 = - 5/2
so
v = 20 - (5/2) t = 20 - (5/2)(time - 5)
physics - Anonymous, Tuesday, June 16, 2015 at 4:02am
68.75m
Slope=AB÷OB
=20m/s÷5s
=4m
-acceleration=retardation
-4m
To draw a graph of velocity against time, we can break down the given information into two parts:
1. First, the car travels at a uniform velocity of 20 m/s for 5 seconds.
The velocity is constant during this period, so the graph will be a horizontal line at 20 m/s for the first 5 seconds.
2. Next, the brakes are applied, and the car comes to rest with uniform retardation in 8 seconds.
Since the car comes to a stop, the velocity will gradually decrease until it reaches zero. The graph will be a downward sloping line, starting from the point where the first section ended.
Now, let's calculate the distance the car travels after the brakes are applied.
In the first section, the car traveled with a uniform velocity of 20 m/s for 5 seconds. Therefore, the distance covered during this period can be calculated using the equation:
Distance = Velocity × Time = 20 m/s × 5 s = 100 meters.
In the second section, the car comes to rest with uniform retardation in 8 seconds. We want to calculate the distance covered during this period. To do so, we first need to find the acceleration using the equation:
Acceleration = Change in Velocity / Time = (0 m/s - 20 m/s) / 8 s = -2.5 m/s^2.
Then, we can use the equation of motion:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2.
Plugging in the values, we get:
Distance = 0 m/s × 8 s + (1/2) × (-2.5 m/s^2) × (8 s)^2 = -80 meters.
The negative sign in the distance indicates that the car traveled in the opposite direction during this period.
To find the total distance traveled after the brakes were applied, we add the individual distances:
Total Distance = Distance in the first section + Distance in the second section
Total Distance = 100 meters + (-80 meters) = 20 meters.
Hence, the car travels a distance of 20 meters after the brakes are applied.