A certain car is capable of accelerating at a uniform rate of #0.85# #m##/##s^2#. What is the magnitude of the car's displacement as it accelerates uniformly from a speed of #83# #km##/##h# to one of #94# #km##/##h#?
1 Answer
Explanation:
We're asked to find the distance a car travels with a given constant acceleration and initial and final velocities.
To find this distance, we'll use the equation
Our known quantities are
-
#a_x = 0.85"m"/("s"^2)# -
#v_x# is the final velocity,#94"km"/"h"# , which me must convert to units of#"m"/"s"# to be consistent:
#((94cancel("km"))/(1cancel("h")))((10^3"m")/(1cancel("km")))((1cancel("h"))/(3600"s")) = color(red)(26.1"m"/"s"#
- The initial velocity
#v_(0x)# ,#83"km"/"h"# , which we must also convert:
#((83cancel("km"))/(1cancel("h")))((10^3"m")/(1cancel("km")))((1cancel("h"))/(3600"s")) = color(blue)(23.1"m"/"s"#
Plugging in the known values, we have
rounded to
During this change in velocity, the car will thus travel a distance of