in 5 seconds, a car moving in a straight line increases it's speed from 50km/h to 65km/h, while a truck goes from rest to 15km/h in a straight line. which undergoes greater acceleration? what is the acceleration of each vehicle?
Car: from 50 km/h INCREASED to 65 km/h, therefore;
65 km/h - 50 km/h = 15 km/h
Truck: from rest (which is 0 km/h) to 15 km/h, therefore;
0 km/h + 15 km/h
The car and the truck both have the same acceleration.
acceleration=(v2-v1)/time
To determine which vehicle undergoes greater acceleration, we can use the formula for acceleration:
Acceleration (a) = Change in velocity (Δv) / Time taken (Δt)
For the car:
Initial velocity (u) = 50 km/h
Final velocity (v) = 65 km/h
Change in velocity (Δv) = v - u = 65 km/h - 50 km/h = 15 km/h
Time taken (Δt) = 5 seconds
Acceleration of the car:
a_car = Δv / Δt = 15 km/h / 5 s = 3 km/h/s
For the truck:
Initial velocity (u) = 0 km/h (truck is at rest)
Final velocity (v) = 15 km/h
Change in velocity (Δv) = v - u = 15 km/h - 0 km/h = 15 km/h
Time taken (Δt) = 5 seconds
Acceleration of the truck:
a_truck = Δv / Δt = 15 km/h / 5 s = 3 km/h/s
Therefore, both the car and the truck undergo the same acceleration of 3 km/h/s, but the car starts with a higher initial velocity.
To determine which vehicle undergoes greater acceleration, we need to calculate the acceleration for each vehicle using the formula:
Acceleration = (Final Speed - Initial Speed) / Time
Let's calculate the acceleration for each vehicle step by step:
1. Car:
Initial Speed (Vi) = 50 km/h
Final Speed (Vf) = 65 km/h
Time (t) = 5 seconds
Acceleration of the car = (Vf - Vi) / t
Acceleration of the car = (65 km/h - 50 km/h) / 5 s
Acceleration of the car = 15 km/h / 5 s
Before we proceed, let's convert the units to a consistent system, such as meters per second (m/s):
1 km/h is equal to 1000 m / 3600 s
So, 15 km/h = (15 * 1000 m) / (3600 s) = 4.17 m/s
Acceleration of the car = 4.17 m/s / 5 s
Acceleration of the car ≈ 0.83 m/s²
2. Truck:
Initial Speed (Vi) = 0 km/h (truck starts from rest)
Final Speed (Vf) = 15 km/h
Time (t) = 5 seconds
Acceleration of the truck = (Vf - Vi) / t
Acceleration of the truck = (15 km/h - 0 km/h) / 5 s
Acceleration of the truck = 15 km/h / 5 s
Again, let's convert the units to m/s:
15 km/h = (15 * 1000 m) / (3600 s) = 4.17 m/s
Acceleration of the truck = 4.17 m/s / 5 s
Acceleration of the truck ≈ 0.83 m/s²
Both the car and the truck have the same acceleration of approximately 0.83 m/s².
Therefore, even though the car underwent a greater increase in speed, both vehicles experienced the same amount of acceleration.