The car stationary in front of a red traffic light. As the light turns green , a truck goes past at a constant velocity of 1.5 m/s. At the same moment , the car begins to accelerate at 1.25 m/s 2 . When it reaches 2.5 m/s the car continues at this velocity . When does the car pass the truck ? How far they gone from the traffic light at that time ?
time it take car to accelerate-2.5/1.25=2sec assume car overtakes truck after tsec Dt=1.5t Dc=(1/2*2*2.5)+2.5(t-2)=2.5t-2.5 At time t,Dt=Dc 1.5t=2.5t-2.5 t=2.5secs b)distance they have travelled equals d=1.5*2.5=3.75m
25 s / 0.38 km
a.25 s
b. 0.38 km
this are the answers, but I don't know the solutions.
To determine when the car passes the truck, we need to find the time it takes for the car to catch up and surpass the truck. Let's break down the problem into different parts:
Part 1: Determining the time it takes for the car to reach 2.5 m/s.
We know that the car starts from rest and accelerates at a rate of 1.25 m/s^2. Using the equation of motion:
v = u + at
where:
v = final velocity (2.5 m/s)
u = initial velocity (0 m/s)
a = acceleration (1.25 m/s^2)
t = time
Rearranging the equation, we have:
t = (v - u) / a
t = (2.5 - 0) / 1.25
t = 2 seconds
So it takes 2 seconds for the car to reach a velocity of 2.5 m/s.
Part 2: Finding the distance traveled by the car and truck during that time.
Since the truck passes the car at a constant velocity of 1.5 m/s, we can calculate how far the truck has traveled in 2 seconds.
Distance = Speed × Time
Distance = 1.5 m/s × 2s
Distance = 3 meters
So the truck has traveled 3 meters during the 2 seconds it took for the car to reach 2.5 m/s.
Part 3: Determining when the car passes the truck.
Now we need to find the time for the car to catch up with and surpass the truck. Since both vehicles are moving at constant velocities, we can assume their speeds remain constant.
Given that the car is continuing at a velocity of 2.5 m/s and the truck is moving at a constant velocity of 1.5 m/s, the car's relative velocity to the truck is:
Relative Velocity = Car's velocity - Truck's velocity
Relative Velocity = 2.5 m/s - 1.5 m/s
Relative Velocity = 1 m/s
To calculate the time it takes for the car to pass the truck, we divide the distance between them by the relative velocity:
Time = Distance / Relative Velocity
Time = 3 meters / 1 m/s
Time = 3 seconds
So the car passes the truck and catches up with it after 3 seconds.
However, we still need to calculate how far they have gone from the traffic light at that time. They have both been moving for a total of 3 seconds, so we need to determine the distance traveled by each vehicle during that time.
For the car:
Distance = Initial velocity × time + 0.5 × acceleration × (time)^2
Distance = 0 m/s × 3 seconds + 0.5 × 1.25 m/s^2 × (3 seconds)^2
Distance = 0 + 0.5 × 1.25 m/s^2 × 9 seconds^2
Distance = 5.625 meters
For the truck:
Distance = Velocity × Time
Distance = 1.5 m/s × 3 seconds
Distance = 4.5 meters
At the time the car passes the truck, the car has traveled approximately 5.625 meters from the traffic light, and the truck has traveled about 4.5 meters.