A bike rider accelerates constantly to a velocity of 9.5m/sec in 6 seconds. The displacement during the acceleration was 36m. What was the initial velocity of the bike?

Answer 1

Note the battery of equations for kinematic motion in one dimension:

v = v₀ + at

x − x₀ = 0.5(v + v₀)t

x − x₀ = v₀t + 0.5at²

v² = v₀² + 2a(x − x₀)

The first conditions given are v = 9.5 meters per second and t = 6 seconds.

Then displacement is given as d = 36 meters.

Scan the battery of equations and place given values wherever possible:

9.5 m/s = v₀ + a(6 s)

36 m = 0.5(9.5 m/s + v₀)(6 s)

36 m = v₀(6 s) + 0.5a(6 s)²

(9.5 m/s)² = v₀² + 2a(36 m)

One can go to the second equation and gain (36 ÷ 0.5 ÷ 6) − 9.5 = v₀,

which forces v₀ to 2.5 meters per second.

Evaluation of 9.5 m/s = v₀ + a(6 s) with v₀ = 2.5 meters per second will also give a as

1.1666666666 meters-per-second-squared.

These values of v₀ and a along with the given values of v, t, and (x − x₀) will give equal outcomes

for each of the four kinematic equations at the top.

Answer 2

Hello, There are a couple of methods to solve this problem, but a substitution is the most straightforward approach.

Here are two equations we need:

First Equation: a = v-u/t, where a is acceleration, u is initial velocity, v is velocity, and t is time.

Second Equation: S = ut + 1/2at^2, where S is displacement, u in initial velocity, t is time, and a is acceleration

Here is what we know from the question: Final velocity(v) is 9.5ms^-1 , time(t) is 6s, and displacement(s) is 36m

On the second equation, you may notice there are two unknowns, the initial velocity, and acceleration, however, if we use a substitution using the first equation, we can get in in terms of only initial velocity.

We know a = 9.5-u / 6, and 36 = 6u + 1/2a(6)^2, from plugging in our knowns.

Now substitute what we know acceleration is (from first equation) in terms of initial velocity into the second equation:

So we have: 36 = 6u + 18 * (9.5-u)/6, after simplifying.

Now continue simplifying and solve for u:

36 = 6u + 28.5 - 3u

36 = 3u + 28.5

7.5 = 3u

u = 2.5 meters per second. Therefore the initial velocity is 2.5 meters per second.

I hope this helped, and if you have any questions or concerns, Ill be sure to reply.