Mathematics (1 Viewer)

[spotspot1]

Hey, much appreciated if you guys solve these questions with working out Answers are there aswel !

Question 1
A ball is rolled up a slope at a distance from the base of the slope, after time t seconds, given by x= 15t-3t^2 meters.
a) how far up the slope will the sole will the ball roll before it starts to roll back down?
b) What will its velocity be when it reaches the base of the slope?
c) How long will the motion of the ball take altogether?

Answers
a) 18.75m
b)-15
c)5 s

Question 2
A weight is on the end of a spring has a height given by h=3sin2t cm where t is time in seconds.
a) find its initial height.
b) Find when the spring is at its maximum distance from the origin?
c) what is the acceleration at these times?

Answers
a) 0 cm (at the origin)
b) pi/4 , 3pi/4 , 5pi/4s
c)12,-12

Question 3
A particle is moving in a straight line so that its displacement x cm over time t seconds is even by
x= t (49-t^2)^1/2
a) For how many seconds does the particle travel?
b)Find the exact time at which the particle comes to rest
c)How far does the particle move altogether?

Answers
a) 7s
b)7/root2
c) 49cm

 

[davidgoes4wce]

Hey, much appreciated if you guys solve these questions with working out Answers are there aswel !

Question 1
A ball is rolled up a slope at a distance from the base of the slope, after time t seconds, given by x= 15t-3t^2 meters.
a) how far up the slope will the sole will the ball roll before it starts to roll back down?
b) What will its velocity be when it reaches the base of the slope?
c) How long will the motion of the ball take altogether?

Answers
a) 18.5m
b)-15
c)5 s

Question 2
A weight is on the end of a spring has a height given by h=3sin2t cm where t is time in seconds.
a) find its initial height.
b) Find when the spring is at its maximum distance from the origin?
c) what is the acceleration at these times?

Answers
a) 0 cm (at the origin)
b) pi/4 , 3pi/4 , 5pi/4s
c)12,-12

Question 3
A particle is moving in a straight line so that its displacement x cm over time t seconds is even by
x= t (49-t^2)^1/2
a) For how many seconds does the particle travel?
b)Find the exact time at which the particle comes to rest
c)How far does the particle move altogether?

Answers
a) 7s
b)7/root2
c) 49cm

This is my graph

 

[davidgoes4wce]

 

[spotspot1]

thank you for correcting , didn't realize i made a mistake

 

[davidgoes4wce]

Hey, much appreciated if you guys solve these questions with working out Answers are there aswel !

Question 2
A weight is on the end of a spring has a height given by h=3sin2t cm where t is time in seconds.
a) find its initial height.
b) Find when the spring is at its maximum distance from the origin?
c) what is the acceleration at these times?

Answers
a) 0 cm (at the origin)
b) pi/4 , 3pi/4 , 5pi/4s
c)12,-12

Question 2 , I assume you are looking for the first 3 times in which the maximum distance occurs.

 

[davidgoes4wce]

Hey, much appreciated if you guys solve these questions with working out Answers are there aswel !

Question 3
A particle is moving in a straight line so that its displacement x cm over time t seconds is even by
x= t (49-t^2)^1/2
a) For how many seconds does the particle travel?
b)Find the exact time at which the particle comes to rest
c)How far does the particle move altogether?

Answers
a) 7s
b)7/root2
c) 49cm

Here are the worked out solutions:

 

[davidgoes4wce]

Guess what?

Its past midnight and I've been up since 6.30am and I still have more motivation

 

[spotspot1]

you've been up early, you should get some sleep tho.
Btw thank you for solving those questions