So basically I got this question and it's baffling. Over a distance of 5m the speed of a bicycle increase's from 2ms to 5ms what I's the magnitude of acceleration?
a = change in v/ change in time
= (5-2)/time
well how long did it take?
average speed = 7/2 =3.5
time = 5/3.5
so
a = 3 /(5/3.5)
= 2.1 m/s^2
You can use average speed with constant acceleration because
v = Vi + a t, straight line
Thanks. I understand it now. But we have like set formulas in our tables for incidence like v=u+at etc. I have learnt the changing velocity over time but in a test situation would I have to use the formulas given or the method appove?
distance from t1 to t2 =
integral v dt = Vi (t2-t1) + .5a (t2-t1)^2
distance/time
= average speed
= Vi + .5 a (t2-t1)
but speed at t2 is v2 = Vi + a (t2-t1)
so a(t2-t1) = v2-vi
so
average speed = Vi + .5(V2-Vi)
= .5 (Vi+V2)
if you really wanted to know :)
Relating to the first question. How long did it take to do this?
well to do the problem with your formulas
v = Vi + a t
5 = 2 + a t
so
3 = a t so t = 3/a
and
d = Vi t + .5 a t^2
5 = 2 t + .5 a t^2
5 = 2 (3/a) + .5 a (9/a^2)
5 = 6/a + 4.5/a
5 a = 10.5
a = 2.1 m/s^2 again
time needed is 3/a
Got the answer it's basically 5-2/2.1=1.43s
To find the magnitude of acceleration, you need to use the equation for acceleration:
acceleration (a) = change in velocity (Δv) / change in time (Δt)
In this case, you are given the initial velocity (2 m/s) and the final velocity (5 m/s), and you know the distance (5 meters) traveled during this time.
First, let's find the change in velocity:
Δv = final velocity - initial velocity
Δv = 5 m/s - 2 m/s
Δv = 3 m/s
Now, we need to find the time it took for the change in velocity to occur. To do this, we can use the formula for average velocity:
average velocity = total distance / total time
Since only the distance is given and we don't have the total time, we need to rearrange the formula to solve for time:
total time = total distance / average velocity
total time = 5 m / (2 m/s) = 2.5 s
Now we have the change in velocity (3 m/s) and the change in time (2.5 s). We can substitute these values into the equation for acceleration to find the magnitude:
acceleration (a) = Δv / Δt
acceleration (a) = 3 m/s / 2.5 s
acceleration (a) = 1.2 m/s²
Therefore, the magnitude of acceleration is 1.2 m/s².