Date | May 2021 | Marks available | 4 | Reference code | 21M.2.AHL.TZ2.6 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 2 |
Command term | Find | Question number | 6 | Adapted from | N/A |
Question
A particle P moves along the x-axis. The velocity of P is v m s−1 at time t seconds, where v=−2t2+16t−24 for t≥0.
Find the times when P is at instantaneous rest.
Find the magnitude of the particle’s acceleration at 6 seconds.
Find the greatest speed of P in the interval 0≤t≤6.
The particle starts from the origin O. Find an expression for the displacement of P from O at time t seconds.
Find the total distance travelled by P in the interval 0≤t≤4.
Markscheme
solving v=0 M1
t=2, t=6 A1
[2 marks]
use of power rule (M1)
(A1)
(A1)
magnitude A1
[4 marks]
using a sketch graph of (M1)
A1
[2 marks]
METHOD ONE
attempt at integration of (M1)
A1
attempt to find (use of ) (M1)
A1
METHOD TWO
attempt at integration of (M1)
A1
attempt to substituted limits into their integral (M1)
A1
[4 marks]
(M1)(A1)
Note: Award M1 for using the absolute value of , or separating into two integrals, A1 for the correct expression.
A1
[3 marks]