Forumla Substitution and relations HELP!

[AR2015]

Can someone please point me in the right direction on this one, not even sure where to start. I have the values as stated in the paragraph below, but not sure where to go with them....

Two cars moving in the same direction pass a point P on a road at the same time. Car A is moving with a constant velocity of 15m/s. Car B has a velocity of 5 m/s at the instant that it passes P and is accelerating at the rate of 1 m/s2. (Note that if a car has constant velocity then its acceleration must be zero).

a. Using the formula s = u t + 12 a t 2 where s is distance from the starting point in metres, u is the velocity initially, a is acceleration in m/s2 and t is time in seconds, write a relationship between s and t for car A and for car B.

b. Calculate the value of t which satisfies both of these equations.

c.What does this value of t mean in relation to the position of the two cars relative to each other?

 

[Deleted member 4993]

Can someone please point me in the right direction on this one, not even sure where to start. I have the values as stated in the paragraph below, but not sure where to go with them....

Two cars moving in the same direction pass a point P on a road at the same time. Car A is moving with a constant velocity of 15m/s. Car B has a velocity of 5 m/s at the instant that it passes P and is accelerating at the rate of 1 m/s2. (Note that if a car has constant velocity then its acceleration must be zero).
a. Using the formula
where s is distance from the starting point in metres, u is the velocity initially, a is
s = u t + 12 a t 2 acceleration in m/s2 and t is time in seconds, write a relationship between s and t for
car A and for car B.
b. Calculate the value of t which satisfies both of these equations.
c.What does this value of t mean in relation to the position of the two cars relative to each other?

What are your thoughts?

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[stapel]

Two cars moving in the same direction pass a point P on a road at the same time. Car A is moving with a constant velocity of 15m/s. Car B has a velocity of 5 m/s at the instant that it passes P and is accelerating at the rate of 1 m/s2. (Note that if a car has constant velocity then its acceleration must be zero).

a. Using the formula s = u t + 12 a t 2 where s is distance from the starting point in metres, u is the velocity initially, a is acceleration in m/s2 and t is time in seconds, write a relationship between s and t for car A and for car B.

Would it be correct to assume that the "2" after the "t" is meant to be an exponent, so the formula is as follows?

. . . . .\(\displaystyle s\, =\, ut\, +\, 12at^2\)

Either way, note that the exercise has given you that:

. . .Car A:
. . . . .initial velocity: v(0) = 15
. . . . .velocity: v(t) = 15
. . . . .acceleration: a(t) = 0

. . .Car B:
. . . . .initial velocity: v(0) = 5
. . . . .velocity: v(t) = v(0) + a(t)*t
. . . . .acceleration: a(t) = 1

You are given a formula for "s" in terms of "t", where certain values need to be filled in. You've been asked to fill in this formula with the given information. How far have you gotten in the plug-n-chug?

b. Calculate the value of t which satisfies both of these equations.

I'm not sure what they're asking for here. Is there a worked example which might explain their meaning?

c.What does this value of t mean in relation to the position of the two cars relative to each other?

I suspect they're looking for the time at which the two cars meet up again. (They started at the same point, P, but Car A is going faster at this point. However, Car A is moving at a fixed speed, while Car B is accelerating. As a result, Car B will eventually catch up to Car A.)

When you reply, please include a clear listing of your efforts so far. Thank you!

 

[Dale10101]

hmmm

Can someone please point me in the right direction on this one, not even sure where to start. I have the values as stated in the paragraph below, but not sure where to go with them....

Two cars moving in the same direction pass a point P on a road at the same time. Car A is moving with a constant velocity of 15m/s. Car B has a velocity of 5 m/s at the instant that it passes P and is accelerating at the rate of 1 m/s2. (Note that if a car has constant velocity then its acceleration must be zero).

a. Using the formula s = u t + 12 a t 2 where s is distance from the starting point in metres, u is the velocity initially, a is acceleration in m/s2 and t is time in seconds, write a relationship between s and t for car A and for car B.

b. Calculate the value of t which satisfies both of these equations.

c.What does this value of t mean in relation to the position of the two cars relative to each other?

s = u t + 12 a t 2 ???

do you mean:

s = ut + (1/2)at² which I believe is the standard kinematic equation for position vs time when a body is undergoing constant acceleration starting from an initial position of s = 0 and an initial velocity of u ?