Question

A particle starts moving on the x-axis at t=0s. Its position at time t is given
by the function: x = 10 − 12t + 5t
2 (where x is in meters and t is in
seconds). How far away from the starting position is the particle at time t =
3 seconds?

Answer 1

Answer:

21 m is the required answer

Step-by-step explanation:

At first put t = 0 and then put =3

then differentiate the distances.

Answer 2

Given:

A particle starts moving on the x-axis at t=0s.

Its position at time t is given by the function: 10 − 12t + 5t²

To Find:

How far away from the starting position is the particle at time t = 3 sec?

Solution:

Now we need to find out the distance of the particle, hence to find that we first need to know what is the position of the particle at t = 0 sec and at t = 3 secs.

To find that we will be using the function given to us in the given,

x = 10 − 12t + 5t²

where x is in meters and t is in seconds

Now at t = 0 sec,

x = 10 − 12t + 5t²

x = 10 − 12 × 0 + 5 × 0²

x = 10 m

Hence, at t = 0 sec, its position is 10 m.

Now for t = 3 secs, we will use the same function,

x = 10 − 12t + 5t²

x = 10 − 12×3 + 5×3²

x = 10 - 36 + 45

x = 19 m

Hence, at t = 3 secs, its position is 19 m.

Hence to find how far is the particle from the starting position, we will subtract the position of the particle at t = 0 sec from the position of the particle at t = 3 secs.

Hence, distance from starting position at t = 3 secs = 19 m - 10 m

                                                                                         = 9 m

The particle is 9 m away from the starting position is the particle at time t = 3 seconds

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