A car traveling 70km/h east changed its velocity to 90km/h east in 4.5s. Determine the magnitude and direction of the average acceleration of the car in m/s2.
If possible can someone explain how to figure this out and not just the answer? And what is the formula for magnitude? I tried looking it up but now I'm twice as confused as I was
To determine the magnitude and direction of the average acceleration of the car, we first need to understand the concept of acceleration and how it is calculated.
Acceleration measures how quickly an object's velocity changes over time. It is the rate at which the velocity of an object changes. Mathematically, acceleration (a) is defined as the change in velocity (Δv) divided by the change in time (Δt). The formula for average acceleration is:
a = Δv / Δt
To calculate the change in velocity, we subtract the initial velocity (v_initial) from the final velocity (v_final). In this case, the initial velocity of the car is 70 km/h east, and the final velocity is 90 km/h east.
Δv = v_final - v_initial
= 90 km/h east - 70 km/h east
Now, we need to convert the velocities from kilometers per hour (km/h) to meters per second (m/s) to ensure consistent units. To convert km/h to m/s, we divide by 3.6 since there are 3.6 seconds in an hour and 1000 meters in a kilometer.
v_initial = 70 km/h east * (1 km/3600 s)
= 19.4 m/s east
v_final = 90 km/h east * (1 km/3600 s)
= 25 m/s east
Substituting these values into the formula for Δv, we have:
Δv = 25 m/s east - 19.4 m/s east
= 5.6 m/s east
Now, let's calculate the change in time (Δt). We are given that the time interval is 4.5 seconds, so:
Δt = 4.5 s
Finally, we can calculate the average acceleration using the formula:
a = Δv / Δt
= 5.6 m/s east / 4.5 s
= 1.24 m/s^2 east
So, the magnitude of the average acceleration is approximately 1.24 m/s^2, and the direction is east.
The formula for magnitude is the absolute value of the vector quantity. In this case, since acceleration is a vector quantity, its magnitude is the absolute value of the average acceleration.
Magnitude of average acceleration (|a|) = |1.24 m/s^2| = 1.24 m/s^2